Boson-Fermion Duality from Discontinuous Gauge Symmetry

TL;DR

This paper demonstrates a duality between bosonic and fermionic systems in quantum mechanics by extending gauge symmetry to include discontinuous transformations, establishing their equivalence in various dimensions.

Contribution

It introduces a novel extension of gauge symmetry to discontinuous transformations, revealing a duality between bosons and fermions in quantum systems.

Findings

Bosonic and fermionic systems are equivalent under certain discontinuous gauge transformations.

The duality extends from one-dimensional to higher-dimensional quantum systems.

Discontinuous gauge symmetry can relate symmetric and antisymmetric wave functions.

Abstract

By extending local U(1) gauge symmetry to discontinuous case, we find that under one special discontinuous U(1) gauge transformation the symmetric and antisymmetric wave functions can transform into each other in one dimensional quantum mechanics. The free spinless fermionic system and bosonic system with $\delta$-type vector gauge potential are proved to be equivalent. The relation also holds in higher space-time dimensions.