The quantum geometry of spin and statistics

Nikolaos Papadopoulos, Andrés Fernando Reyes-Lega

Jouko Mickelsson

The spin and statistics connection is examined in classical point-particle mechanics in the spirit of the field-theoretic homotopy proof for the spin-statistics theorem by Finkelstein and Rubinstein. The theorem is proven when the geometry of the configuration space is determined by a parallelization describing a soliton field. It is indicated how the characteristic features of the system can be preserved in the corresponding quantized (nonrelativistic) system.

Arthur Jabs

Karl Gustafson

Chavis Srichan

This study performs a comprehensive statistical comparison between predictions derived from Entanglement-Weighted Operator Geometry (EWOG) and traditional Condensed Matter (CM) physics models. Using experimental data from three paradigmatic quantum material classes—heavy-fermion systems, quantum spin liquids, and unconventional superconductors—we apply information-theoretic criteria (AIC, BIC), Bayesian model selection, and frequentist hypothesis testing. Our analysis demonstrates that EWOG models consistently provide superior fits to experimental data with greater parameter efficiency. For $\mathrm{CeCoIn}_{5}$ specific heat data, EWOG yields $\Delta\text{AIC} = 14.5$ and Bayes factor $>10^3$ versus the best CM model. We present complete numerical derivations of all statistical tests, establishing EWOG as a statistically superior framework for describing emergent phenomena in strongly correlated quantum matter.

James Thomas Wheeler