Tootfinder

The MODEST catalog of depth-dependent spatially coupled inversions of sunspots observed by Hinode/SOT-SP
J. S. Castellanos Dur\'an, N. Milanovic, A. Korpi-Lagg, B. L\"optien, M. van Noort, S. K. Solanki
https://arxiv.org/abs/2403.06960

The MODEST catalog of depth-dependent spatially coupled inversions of sunspots observed by Hinode/SOT-SP
We present a catalog that we named MODEST containing depth-dependent information on the atmospheric conditions inside sunspot groups of all types. The catalog is currently composed of 942 observations of 117 individual active regions with sunspots that cover all types of features observed in the solar photosphere. We use the SPINOR-2D code to perform spatially coupled inversions of the Stokes profiles observed by Hinode/SOT-SP at high spatial resolution. SPINOR-2D accounts for the unavoidable d…

This https://arxiv.org/abs/2401.13909 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

A Spinorial proof of the positivity of Quasi-Local mass
We provide spinor-based proof of the positivity of the Wang-Yau \cite{yau} quasi-local mass. More precisely we prove under an appropriate spin assumption that the gravitational mass bounded by a spacelike topological $2-$sphere is non-negative in a generic spacetime verifying dominant energy condition and vanishes only if the surface is embedded in the Minkowski space. This proof is purely quasi-local in nature and in particular does not rely on Bartanik's gluing and asymptotic extension constr…

This https://arxiv.org/abs/2303.14181 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_hept…

Transformations of Currents in Sigma-Models with Target Space Supersymmetry
We develop a framework for systematic study of symmetry transformations of sigma-model currents in a special situation, when symmetries have a well-defined projection onto the target space. We then apply this formalism to pure spinor sigma-models, and describe the resulting geometric structures in the target space (which in our approach includes the pure spinor ghosts). We perform a detailed study of the transformation properties of currents, using the formalism of equivariant cohomology. We cl…

The MODEST catalog of depth-dependent spatially coupled inversions of sunspots observed by Hinode/SOT-SP
J. S. Castellanos Dur\'an, N. Milanovic, A. Korpi-Lagg, B. L\"optien, M. van Noort, S. K. Solanki
https://arxiv.org/abs/2403.06960

The MODEST catalog of depth-dependent spatially coupled inversions of sunspots observed by Hinode/SOT-SP
We present a catalog that we named MODEST containing depth-dependent information on the atmospheric conditions inside sunspot groups of all types. The catalog is currently composed of 942 observations of 117 individual active regions with sunspots that cover all types of features observed in the solar photosphere. We use the SPINOR-2D code to perform spatially coupled inversions of the Stokes profiles observed by Hinode/SOT-SP at high spatial resolution. SPINOR-2D accounts for the unavoidable d…

This https://arxiv.org/abs/2211.03987 has been replaced.
link: https://scholar.google.com/scholar?q=a

Theta series of ternary quadratic lattice cosets
In this paper, we consider the decomposition of theta series for lattice cosets of ternary lattices. We show that the natural decomposition into an Eisenstein series, a unary theta function, and a cuspidal form which is orthogonal to unary theta functions correspond to the theta series for the genus, the deficiency of the theta series for the spinor genus from that of the genus, and the deficiency of the theta series for the class from that of the spinor genus, respectively. These three pieces …

Adinkras and Pure Spinors
Richard Eager, Simone Noja, Raphael Senghaas, Johannes Walcher
https://arxiv.org/abs/2404.07167 https://arx…

Adinkras and Pure Spinors
The nilpotence variety for extended supersymmetric quantum mechanics is a cone over a quadric in projective space. The pure spinor correspondence, which relates the description of off-shell supermultiplets to the classification of modules over the corresponding hypersurface ring, reduces to a classical problem of linear algebra. Spinor bundles, which correspond to maximal Cohen-Macaulay modules, serve as basic building blocks. Koszul duality appears as a deformed version of the Bernstein-Gel'fa…

This https://arxiv.org/abs/2307.05932 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_hept…

Lorentz-covariant spinor wave packet
We propose a new formulation of manifestly Lorentz-covariant spinor wave-packet basis. The conventional definition of the spinor wave packet is problematic in the sense that it suffers from mixing with other wave packets under Lorentz transformations. Our formulation evades this difficulty of mixing. This wave packet forms a complete set that can expand a free spinor field in a Lorentz covariant manner. In addition, we present a Lorentz-invariant expression of zero-point energy.

Differential spinors and Kundt three-manifolds with skew-torsion
C. S. Shahbazi
https://arxiv.org/abs/2405.03756 https://arxiv.org/pd…

Differential spinors and Kundt three-manifolds with skew-torsion
We develop the theory of spinorial polyforms associated with bundles of irreducible Clifford modules of non-simple real type, obtaining a precise characterization of the square of an irreducible real spinor in signature $(p-q) = 1\,\mathrm{mod(8)}$ as a polyform belonging to a semi-algebraic real set. We use this formalism to study differential spinors on Lorentzian three-manifolds, proving that in this dimension and signature, every differential spinor is equivalent to an isotropic line preser…

This https://arxiv.org/abs/2403.17029 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_qu…

Relativistic exponential-type spinor orbitals and their use in many-electron Dirac equation solution
Dirac-Coulomb type differential equation and its solution relativistic exponential-type spinor orbitals are introduced. They provide a revised form for operator invariants, namely Dirac invariants, simplifying the treatment of the angular components in calculation of many-electron systems. The relativistic Coulomb energy is determined by employing a spectral solution to Poisson's equation for the one$-$electron potential, which is expressed in terms of radial functions involving incomplete gamm…

This https://arxiv.org/abs/2404.04777 has been replaced.
initial toot: https://mastoxiv.page/@arX…

Variational Improvement of the Hartree-Fock Approach to the 2D Hubbard Model
We consider a refinement of the usual Hartree-Fock method applied the 2D Hubbard model, in Nambu spinor formulation. The new element is the addition of a ''condensate inducing'' term proportional to a variational parameter h to the Hartree-Fock Hamiltonian, which generates an s- or d-wave condensate. This modified Hartree-Fock Hamiltonian is used only to generate variational trial states; energy expectation values are computed in the full two-dimensional Hubbard Hamiltonian with no modification…

A new computational framework for spinor-based relativistic exact two-component calculations using contracted basis functions
Chaoqun Zhang, Kirk A. Peterson, Kenneth G. Dyall, Lan Cheng
https://arxiv.org/abs/2405.04008

A new computational framework for spinor-based relativistic exact two-component calculations using contracted basis functions
A new computational framework for spinor-based relativistic exact two-component (X2C) calculations is developed using contracted basis sets with a spin-orbit contraction scheme. Generally contracted j-adapted basis sets using primitive functions in the correlation-consistent basis sets are constructed for the X2C Hamiltonian with atomic mean-field spin-orbit integrals (the X2CAMF scheme). The contraction coefficients are taken from atomic X2CAMF Hartree-Fock spinors, hereby following the simple…

Quadratic Spinor Polynomials with Infinitely Many Factorizations
Zijia Li, Hans-Peter Schr\"ocker, Johannes Siegele, Daren A. Thimm
https://arxiv.org/abs/2402.14347

Quadratic Spinor Polynomials with Infinitely Many Factorizations
Spinor polynomials are polynomials with coefficients in the even sub-algebra of conformal geometric algebra whose norm polynomial is real. They describe rational conformal motions. Factorizations of spinor polynomial corresponds to the decomposition of the rational motion into elementary motions. Generic spinor polynomials allow for a finite number of factorizations. We present two examples of quadratic spinor polynomials that admit infinitely many factorizations. One of them, the circular tran…

Unvortex Lattice and Topological Defects in Rigidly Rotating Multicomponent Superfluids
Roy Rabaglia, Ryan Barnett, Ari M. Turner
https://arxiv.org/abs/2404.05857

Unvortex Lattice and Topological Defects in Rigidly Rotating Multicomponent Superfluids
By examining the characteristics of a rotating ferromagnetic spinor condensate through the perspective of large spin, we uncover a novel kind of topological point defect in the magnetization texture. These defects are predicted not by the conventional homotopy group analysis but by the Riemann-Hurwitz formula. The spin texture in the system is described by an equal-area mapping from the plane to the sphere of magnetization, forming a lattice of uniformly charged Skyrmions. This lattice carries …

This https://arxiv.org/abs/2305.00106 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_hept…

Massless Rarita-Schwinger equations: Half and three halves spin solution
Counting the degrees of freedom of the massless Rarita-Schwinger theory is revisited using Behrends-Fronsdal projectors. The identification of the gauge invariant part of the vector-spinor is thus straightforward, consisting of spins 1/2 and 3/2. The validity of this statement is supported by the explicit solution found in the standard gamma-traceless gauge. Since the obtained systems are deterministic -- free of arbitrary functions of time -- we argue that the often-invoked residual gauge symm…

Many-body quantum dynamics of spin-orbit coupled Andreev states in a Zeeman field
Kateryna Zatsarynna, Andrea Nava, Alex Zazunov, Reinhold Egger
https://arxiv.org/abs/2404.05485 <…

Many-body quantum dynamics of spin-orbit coupled Andreev states in a Zeeman field
We provide a theoretical framework to describe the quantum many-body dynamics of Andreev states in Josephson junctions with spin-orbit coupling and a magnetic Zeeman field. In such cases, employing a doubled Nambu spinor description is technically advantageous but one then has to be careful to avoid double-counting problems. By deriving the Lindblad master equation in the socalled excitation picture, we show that a physically consistent many-body theory free from doublecounting problems follows…

Spinor-valued Higgs fields
Nigel Hitchin
https://arxiv.org/abs/2404.12981 https://arxiv.org/pdf/2404.12981

Spinor-valued Higgs fields
We investigate the geometry of holomorphic vector bundles $E$ over a Riemann surface $C$ together with a section of the endomorphism bundle tensored with $K^{1/2}$ -- a square root of the canonical bundle $K$. These parallel to some extent the various features of usual Higgs bundles, such as spectral curve constructions, but some features are radically different. We make essential use of the mod 2 index to distinguish two families of moduli spaces, and provide examples in low genus.

This https://arxiv.org/abs/2402.11593 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_grqc_…

Spacetime geometry from Dirac spinor theory
The quintet of Dirac $4\times 4$ matrices suggests that the fundamental dimension of the internal (spin) space is $n=5$, instead of the conventional dimension $n=4$. Then extending the usual $4\times 4$ tetrads (vierbein), gravity is described in terms of the 5-bein (fünfbein or five legs). We discuss the properties of the spacetime geometry induced from this 5-leg Dirac spinor theory, where the spin connection contains $10\times 4=40$ elements instead of 24 elements in the tetrad formulation …

Hyperbolic Jacobsthal Spinor Sequences and Their Mathematical Properties
Selime Beyza \"Oz\c{c}evik, Abdullah Dertli
https://arxiv.org/abs/2403.14632 …

Hyperbolic Jacobsthal Spinor Sequences and Their Mathematical Properties
In this study, novel Hyperbolic spinor sequences of Jacobsthal, Jacobsthal-Lucas and Jacobsthal polynomial, which have not been studied before, are defined by investigating the relationship between spinors, which are important mathematical objects used in physics and mathematics, and split Jacobsthal and split Jacobsthal-Lucas quaternions, which are extensions of the known Jacobsthal and Jacobsthal-Lucas numbers to quaternion algebra. The recurrence relations of sequences whose members are Hype…

This https://arxiv.org/abs/2402.12456 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_hept…

Three point interaction of Dirac fermions with higher spin particles and discrete symmetries
We constructed all possible kinematically allowed three-point interactions of two massless Dirac spinors with massive higher-spin bosons. In any $D$ spacetime, the interactions have been constructed using the projections of the massive higher spin representations of $Spin(D-1)$ over the massless complex spinor representations of $Spin(D-2)\times Spin(D-2)$. Based on this analysis, we have further classified the space of theories involving one massless Dirac spinor and a single (or multiple) mas…

This https://arxiv.org/abs/2404.12937 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Coupled $\operatorname{G}_2$-instantons
We introduce the coupled instanton equations for a metric, a spinor, a three-form, and a connection on a bundle, over a spin manifold. Special solutions in dimensions $6$ and $7$ arise, respectively, from the Hull--Strominger and the heterotic $\operatorname{G}_2$ system. The equations are motivated by recent developments in theoretical physics and can be recast using generalized geometry; we investigate how coupled instantons relate to generalized Ricci-flat metrics and also to Killing spinors…

This https://arxiv.org/abs/2403.17029 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_qu…

Relativistic exponential-type spinor orbitals and their use in many-electron Dirac equation solution
Dirac-Coulomb type differential equation and its solution relativistic exponential-type spinor orbitals are introduced. They provide a revised form for operator invariants, namely Dirac invariants, simplifying the treatment of the angular components in calculation of many-electron systems. The relativistic Coulomb energy is determined by employing a spectral solution to Poisson's equation for the one$-$electron potential, which is expressed in terms of radial functions involving incomplete gamm…

Chaos-assisted Turbulence in Spinor Bose-Einstein Condensates
Jongmin Kim, Jongheum Jung, Junghoon Lee, Deokhwa Hong, Yong-il Shin
https://arxiv.org/abs/2403.00524

Chaos-assisted Turbulence in Spinor Bose-Einstein Condensates
We present a turbulence-sustaining mechanism in a spinor Bose-Einstein condensate, which is based on the chaotic nature of internal spin dynamics. Magnetic driving induces a complete chaotic evolution of the local spin state, thereby continuously randomizing the spin texture of the condensate to maintain the turbulent state. We experimentally demonstrate the onset of turbulence in the driven condensate as the driving frequency changes and show that it is consistent with the regular-to-chaotic t…

Weighted low-lying zeros of L-functions attached to Siegel modular forms
Shifan Zhao
https://arxiv.org/abs/2403.19687 https://arxiv.o…

Weighted low-lying zeros of L-functions attached to Siegel modular forms
In this paper, we study weighted low-lying zeros of spinor and standard $L$-functions attached to degree 2 Siegel modular forms. We show the symmetry type of weighted low-lying zeros of spinor $L$-functions is symplectic, for test functions whose Fourier transform have support in $(-1,1)$, extending the previous range $(-\frac{4}{15},\frac{4}{15})$ by E. Kowalski, A. Saha and J. Tsimerman . We then show the symmetry type of weighted low-lying zeros of standard $L$-functions is also symplectic. …

This https://arxiv.org/abs/2302.08473 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_hept…

Emergent spinor fields from exotic spin structures
The classification of emergent spinor fields according to modified bilinear covariants is scrutinized, in spacetimes with nontrivial topology, which induce inequivalent spin structures. Extended Clifford algebras, constructed by equipping the underlying spacetime with an extended bilinear form with additional terms coming from the nontrivial topology, naturally yield emergent extended algebraic spinor fields and their subsequent extended bilinear covariants, which are contrasted to the classica…

This https://arxiv.org/abs/2402.07965 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_grqc_…

Extension of Theory of Gravitomagnetism and Spinor Quantum Mechanics with Dynamics of Free Electromagnetic Field
The theory of Gravitomagnetism and spinor quantum mechanics describing the interaction between the Dirac spinor field, the electromagnetic field, and a weak gravitational field is extended by including the Lagrangian density of the free electromagnetic field. It is shown that the newly added term in the Lagrangian density is necessary to restore a symmetric energy-momentum tensor in the interaction term of the Lagrangian density within the theory. We prove that when the electromagnetic energy t…

Determinants of pseudo-laplacians and $\zeta^{({\rm reg})}(1)$ for spinor bundles over Riemann surfaces
Alexey Kokotov, Dmitrii Korikov
https://arxiv.org/abs/2403.12472

Determinants of pseudo-laplacians and $ζ^{({\rm reg})}(1)$ for spinor bundles over Riemann surfaces
Let $P$ be a point of a Riemann surface $X$. We study self-adjoint extensions of Dolbeault Laplacians in hermitian line bundles $L$ over $X$ initially defined on sections with compact supports in $X\backslash\{P\}$. We define the $ζ$-regularized determinants for these operators and derive the comparison formulas for them. We introduce the notion of the Robin mass of $L$. This quantity enters the comparison formulas for determinants and is related to the regularized $ζ(1)$ for the Dolbeault La…

This https://arxiv.org/abs/2403.11181 has been replaced.
initial toot: https://mastoxiv.page/@arX…

Solving Maxwell's Equations
This paper discusses the use of the Riemann-Silberstein vector to solve the source-free Maxwell's equations and obtains novel analytical solutions. The solving process naturally leads to the spinor form of the source-free Maxwell's equations. Several powerful theorems are established to solve this spinor form equation. The Waveguide Solution Theorem provides an elegant way to solve waveguide problems, while The Schrodinger Solution Theorem connects the Maxwell's equations with the two-dimension…

Multiple higher-order poles solutions in spinor Bose-Einstein condensates
Huan Liu, Jing Shen, Xianguo Geng
https://arxiv.org/abs/2402.08362 https://

Multiple higher-order poles solutions in spinor Bose-Einstein condensates
In this study, we explore multiple higher-order pole solutions in spinor Bose--Einstein condensates. These solutions are associated with different pairs of higher-order poles of the transmission coefficient in the inverse scattering transform, and they represent solutions of the spin-1 Gross--Pitaevskii equation. We introduce a direct scattering map that maps initial data to scattering data, which includes discrete spectrums, reflection coefficients, and a polynomial that replaces normalization…

Geometrisation of Fermions in Flat Spacetimes
William J. Leigh
https://arxiv.org/abs/2404.03360 https://arxiv.org/pdf/2404.03360

Geometrisation of Fermions in Flat Spacetimes
Requiring physical consistency in a classical flat spacetime geometrisation of fermions is shown to suggest the introduction of torsion. A resulting simple model for that torsion produces a localised quantum-like particle as a solution of a spinor identity that closely resembles the Dirac equation of quantum electrodynamics. All relevant integrals involving solutions of the spinor identity converge and require that the spin, which is no longer intrinsic but arises from circulating currents, be …

QCD Kondo effect for single heavy quark in chiral-symmetry broken phase
Shigehiro Yasui, Daiki Suenaga, Kei Suzuki
https://arxiv.org/abs/2402.11578 https:/…

QCD Kondo effect for single heavy quark in chiral-symmetry broken phase
We consider the QCD Kondo effect for a single heavy quark in quark matter composed of light quarks with chiral symmetry breaking. Introducing several spinor structures in QCD Kondo condensates, i.e., particle-projected condensate, antiparticle-projected condensate, and normal condensate without projection, we calculate the attractive energy gained by the heavy quark within the mean-field approximation in the path-integral formalism. We show that the normal condensate is favored at low density a…

Laplacians in spinor bundles over translation surfaces: self-adjoint extentions and regularized determinants
Alexey Kokotov, Dmitrii Korikov
https://arxiv.org/abs/2402.12529

Laplacians in spinor bundles over translation surfaces: self-adjoint extentions and regularized determinants
We study the regularized determinants ${\rm det}\, Δ$ of various self-adjoint extensions of symmetric Laplacians acting in spinor bundles over compact Riemann surfaces with flat singular metrics $|ω|^2$, where $ω$ is a holomorphic one form on the Riemann surface. We find an explicit expression for ${\rm det}\, Δ$ for the so-called self-adjoint Szegö extension through the Bergman tau-function on the moduli space of Abelian differentials and the theta-constants (corresponding to th…

Quantum droplets with magnetic vortices in spinor dipolar Bose-Einstein condensates
Shaoxiong Li, Hiroki Saito
https://arxiv.org/abs/2402.18885 https://

Quantum droplets with magnetic vortices in spinor dipolar Bose-Einstein condensates
Motivated by the recent experimental realization of a Bose-Einstein condensate (BEC) of europium atoms, we investigate the self-bound droplet state of a europium BEC with spin degrees of freedom. Under a sufficiently weak magnetic field, the droplet has a torus shape with circulating spin vectors, which is referred to as a magnetic vortex. The ground state transforms from the torus to cigar shape through bistability with an increase in the magnetic field. Dynamical change of the magnetic field …

Topological Noetherianity of the infinite half-spin representations
Christopher Chiu, Jan Draisma, Rob Eggermont, Tim Seynnaeve, Nafie Tairi
https://arxiv.org/abs/2403.10274

Topological Noetherianity of the infinite half-spin representations
We prove that the infinite half-spin representations are topologically Noetherian with respect to the infinite spin group. As a consequence we obtain that half-spin varieties, which we introduce, are defined by the pullback of equations at a finite level. The main example for such varieties is the infinite isotropic Grassmannian in its spinor embedding, for which we explicitly determine its defining equations.

Nonadiabatic quantum Vlasov equation in spinor QED
Z. L. Li, Y. J. Li
https://arxiv.org/abs/2403.10870 https://arxiv.org/pdf/2403.108…

Nonadiabatic quantum Vlasov equation in spinor QED
The nonadiabatic quantum Vlasov equation in spinor QED is derived, and its relation to the well-known adiabatic one is established by three methods. One is by an explicitly analytical expression, the second is by the Dirac equation in the V gauge, and the last is by introducing a turn-off electric field. Wherein what the first two of them are given is an instantaneous relation. Moreover, the time evolution of the distribution function for a specific momentum and the momentum distribution of cre…

This https://arxiv.org/abs/2403.12472 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Determinants of pseudo-laplacians and $ζ^{({\rm reg})}(1)$ for spinor bundles over Riemann surfaces
Let $P$ be a point of a Riemann surface $X$. We study self-adjoint extensions of Dolbeault Laplacians in hermitian line bundles $L$ over $X$ initially defined on sections with compact supports in $X\backslash\{P\}$. We define the $ζ$-regularized determinants for these operators and derive the comparison formulas for them. We introduce the notion of the Robin mass of $L$. This quantity enters the comparison formulas for determinants and is related to the regularized $ζ(1)$ for the Dolbeault La…

This https://arxiv.org/abs/2209.04396 has been replaced.
link: https://scholar.google.com/scholar?q=a

Supersymmetric Kundt four manifolds and their spinorial evolution flows
We investigate the differential geometry and topology of four-dimensional Lorentzian manifolds $(M,g)$ equipped with a real Killing spinor $\varepsilon$, where $\varepsilon$ is defined as a section of a bundle of irreducible real Clifford modules satisfying the Killing spinor equation with non-zero real constant. Such triples $(M,g,\varepsilon)$ are precisely the supersymmetric configurations of minimal four-dimensional supergravity and necessarily belong to the class Kundt of space-times, henc…

Engineering and Revealing Dirac Strings in Spinor Condensates
Gui-Sheng Xu, Mudit Jain, Xiang-Fa Zhou, Guang-Can Guo, Mustafa A. Amin, Han Pu, Zheng-Wei Zhou
https://arxiv.org/abs/2402.14705

Engineering and Revealing Dirac Strings in Spinor Condensates
Artificial monopoles have been engineered in various systems, yet there has been no systematic study on the singular vector potentials associated with the monopole field. We show that the Dirac string, the line singularity of the vector potential, can be engineered, manipulated, and made manifest in a spinor atomic condensate. We elucidate the connection among spin, orbital degrees of freedom, and the artificial gauge, and reveal that there exists a mapping between the vortex filament and the D…

This https://arxiv.org/abs/2404.13455 has been replaced.
initial toot: https://mastoxiv.page/@a…

Adiabatic Approximation and Aharonov-Casher Bands in Twisted Homobilayer TMDs
Topological flat moiré bands with nearly ideal quantum geometry have been identified in AA homobilayer transition metal dichalcogenide moiré superlattices, and are thought to be crucial for understanding the fractional Chern insulating states recently observed therein. Previous work proposed viewing the system using an adiabatic approximation that replaces the position-dependence of the layer spinor by a nonuniform periodic effective magnetic field. When the local zero-point kinetic energy of…

Solving Maxwell's Equations
Tong Chern
https://arxiv.org/abs/2403.11181 https://arxiv.org/pdf/2403.11181

Solving Maxwell's Equations
This paper discusses the use of the Riemann-Silberstein vector to solve the source-free Maxwell's equations and obtains novel analytical solutions. The solving process naturally leads to the spinor form of the source-free Maxwell's equations. Several powerful theorems are established to solve this spinor form equation. The Waveguide Solution Theorem provides an elegant way to solve waveguide problems, while The Schrodinger Solution Theorem connects the Maxwell's equations with the two-dimension…

This https://arxiv.org/abs/2307.13357 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_hept…

Correlation function of flavored fermion in holographic QCD
By using the gauge-gravity duality, we investigate the correlation function of flavored fermion in the \mathrm{D}_{p}/\mathrm{D}_{p+4} model as top-down approaches of holographic QCD for p=4,3. The bulk spinor, as the source of the flavored fermion in QCD, is identified to the worldvolume fermion on the flavor \mathrm{D}_{p+4}-branes and the standard form of its action can be therefore obtained by the T-duality rules in string theory. Keeping this in hand, we afterwards generalize the prescript…

This https://arxiv.org/abs/2310.19900 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_grqc_…

New spinorial mass-quasilocal angular momentum inequality for initial data with marginally future trapped surface
We prove a new geometric inequality that relates the Arnowitt-Deser-Misner mass of initial data to a quasilocal angular momentum of a marginally future trapped surface inner boundary. The inequality is expressed in terms of a 1-spinor, which satisfies an intrinsic first-order Dirac-type equation. Furthermore, we show that if the initial data is axisymmetric, then the divergence-free vector used to define the quasilocal angular momentum cannot be a Killing field of the generic boundary.

This https://arxiv.org/abs/2404.13455 has been replaced.
initial toot: https://mastoxiv.page/@a…

Adiabatic Approximation and Aharonov-Casher Bands in Twisted Homobilayer TMDs
Topological flat moiré bands with nearly ideal quantum geometry have been identified in AA homobilayer transition metal dichalcogenide moiré superlattices, and are thought to be crucial for understanding the fractional Chern insulating states recently observed therein. Previous work proposed viewing the system using an adiabatic approximation that replaces the position-dependence of the layer spinor by a nonuniform periodic effective magnetic field. When the local zero-point kinetic energy of…

Solving Maxwell's Equations
Tong Chern
https://arxiv.org/abs/2403.11181 https://arxiv.org/pdf/2403.11181

Solving Maxwell's Equations
This paper discusses the use of the Riemann-Silberstein vector to solve the source-free Maxwell's equations and obtains novel analytical solutions. The solving process naturally leads to the spinor form of the source-free Maxwell's equations. Several powerful theorems are established to solve this spinor form equation. The Waveguide Solution Theorem provides an elegant way to solve waveguide problems, while The Schrodinger Solution Theorem connects the Maxwell's equations with the two-dimension…

Understanding Fermionic Generalized Symmetries
Federico Ambrosino, Ran Luo, Yi-Nan Wang, Yi Zhang
https://arxiv.org/abs/2404.12301 https://

Understanding Fermionic Generalized Symmetries
We explore new aspects of internal fermionic shifting symmetries, present in physical systems such as free Dirac spinors and p-form tensor-spinor fields. We propose a novel procedure to gauge these global symmetries, which also introduces a new Stückelberg mechanism to give a mass to free fermionic fields. Furthermore, we find new magnetic fermionic symmetries in these physical systems whose charged objects are disorder operators. For the case of a Dirac spinor, we discuss an dual description,…

Fermions in the 6D Standing Wave Braneworld with Real Scalar Field
Pavle Midodashvili
https://arxiv.org/abs/2402.17869 https://arxiv.…

Fermions in the 6D Standing Wave Braneworld with Real Scalar Field
In the article, we investigate localization problem for spinor fields within the 6D standing wave braneworld with the bulk real scalar field, introduced earlier in [30], and explicitly show that there is no normalizable fermion field zero mode trapped on the brane.

This https://arxiv.org/abs/2305.00913 has been replaced.
initial toot: https://mastoxiv.page/@a…

An algorithm for exact analytical solutions for tilted anisotropic Dirac materials
In this article, we obtain the exact solutions for bound states of tilted anisotropic Dirac materials under the action of external electric and magnetic fields with translational symmetry. In order to solve the eigenvalue equation that arises from the effective Hamiltonian of these materials, we describe an algorithm that allow us to decouple the differential equations that are obtained for the spinor components.

This https://arxiv.org/abs/2401.04548 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Generalised Killing Spinors on Three-Dimensional Lie Groups
For each $n\in\mathbb{N}$, we construct a Riemannian spin manifold carrying a generalised Killing spinor with $n$ distinct eigenvalues, providing the first known examples of such objects for $n>4$. For each left-invariant metric on a three-dimensional Lie group, we explicitly find all invariant generalised Killing spinors. We find many new examples with three distinct eigenvalues, and we prove that, in some cases, this is the generic situation.

This https://arxiv.org/abs/2402.10976 has been replaced.
initial toot: https://mastoxiv.page/@arX…

Dirac field, van der Waals gas, Weyssenhoff fluid, Newton particle
We consider the Dirac field in polar formulation, showing that when torsion is taken in effective approximation the theory has the thermodynamic properties of a van der Waals gas, that when the limit of zero chiral angle is taken the theory reduces to that of a Weyssenhoff fluid, and that under the spinless condition it gives the Newtonian particle. This nesting of approximations will allow us to interpret the various objects pertaining to the spinor, with torsion providing a form of negative p…

Spinorial Yamabe-type equations and the B\"ar-Hijazi-Lott invariant
Jurgen Julio-Batalla
https://arxiv.org/abs/2402.10297 https://

Spinorial Yamabe-type equations and the Bär-Hijazi-Lott invariant
We consider on a closed Riemannian spin manifold $(M^n,g,σ)$ the spinorial Yamabe type equation $D_gφ=λ|φ|^{\frac{2}{n-1}}φ$, where $φ$ is a spinor field and $λ$ is a positive constant. For a normalized solution $φ$ of this equation we find a positive lower bound for $λ^2$. As an application we obtain an explicit lower bound of the Bär-Hijazi-Lott invariant for some spin manifolds with positive scalar curvature.

This https://arxiv.org/abs/2307.10040 has been replaced.
initial toot: https://mastoxiv.page/@…

Data-driven discovery of statistically relevant information in quantum simulators
Quantum simulators offer powerful means to investigate strongly correlated quantum matter. However, interpreting measurement outcomes in such systems poses significant challenges. Here, we present a theoretical framework for information extraction in synthetic quantum matter, illustrated for the case of a quantum quench in a spinor Bose-Einstein condensate experiment. Employing non-parametric unsupervised learning tools that provide different measures of information content, we demonstrate a sy…

Dirac field, van der Waals gas, Weyssenhoff fluid, Newton particle
Luca Fabbri
https://arxiv.org/abs/2402.10976 https://arxiv.org/pdf…

Dirac field, van der Waals gas, Weyssenhoff fluid, Newton particle
We consider the Dirac field in polar formulation, showing that when torsion is taken in effective approximation the theory has the thermodynamic properties of a van der Waals gas, that when the limit of zero chiral angle is taken the theory reduces to that of a Weyssenhoff fluid, and that under the spinless condition it gives the Newtonian particle. This nesting of approximations will allow us to interpret the various objects pertaining to the spinor, with torsion providing a form of negative p…

Generating functional of correlators of twist-$2$ operators in $\mathcal{N} = 1$ SUSY Yang-Mills theory, I
Marco Bochicchio, Mauro Papinutto, Francesco Scardino
https://arxiv.org/abs/2403.09617

Generating functional of correlators of twist-$2$ operators in $\mathcal{N} = 1$ SUSY Yang-Mills theory, I
Extending our previous work in pure Yang-Mills (YM) theory, we compute the generating functional of correlators of collinear twist-$2$ operators that enter the components of balanced superfields -- i.e., superfields with an equal number of dotted and undotted indices in their spinor representation -- in $\mathcal{N} = 1$ SUSY SU($N$) YM theory in Minkowskian and Euclidean space-time, in the conformal limit and renormalization-group improved form, and to the leading and next-to-leading order in …