Tootfinder

Graphs With Polarities
John C. Baez, Adittya Chaudhuri
https://arxiv.org/abs/2506.23375 https://arxiv.org/pdf/2506.23375

Graphs With Polarities
In fields ranging from business to systems biology, directed graphs with edges labeled by signs are used to model systems in a simple way: the nodes represent entities of some sort, and an edge indicates that one entity directly affects another either positively or negatively. Multiplying the signs along a directed path of edges lets us determine indirect positive or negative effects, and if the path is a loop we call this a positive or negative feedback loop. Here we generalize this to graphs …

Second Quantization for the Kepler Problem
John C. Baez
https://arxiv.org/abs/2507.11428 https://arxiv.org/pdf/2507.11428

Second Quantization for the Kepler Problem
The Kepler problem concerns a point particle in an attractive inverse square force. After a brief review of the classical and quantum versions of this problem, focused on their hidden $\text{SU}(2) \times \text{SU}(2)$ symmetry, we discuss the quantum Kepler problem for a spin-$\frac{1}{2}$ particle. We show that the Hilbert space $\mathcal{H}$ of bound states for this problem is unitarily equivalent, as a representation of $\text{SU}(2) \times \text{SU}(2)$, to the Hilbert space of solutions o…