Symmetries and classical quantization

TL;DR

The paper explores a classical quantization phenomenon in pseudoclassical gauge systems, showing how specific parameter values enhance symmetries at both classical and quantum levels, with implications for models of massive fermions and gauge fields.

Contribution

It identifies special parameter values that maximize symmetries in pseudoclassical gauge systems and demonstrates their significance in quantum conservation laws.

Findings

Special parameter values lead to maximal symmetries.

Discrete symmetries are conserved at quantum level for specific parameters.

The phenomenon applies to models of massive fermions and gauge fields.

Abstract

A phenomenon of classical quantization is discussed. This is revealed in the class of pseudoclassical gauge systems with nonlinear nilpotent constraints containing some free parameters. Variation of parameters does not change local (gauge) and discrete symmetries of the corresponding systems, but there are some special discrete values of them which give rise to the maximal global symmetries at the classical level. Exactly the same values of the parameters are separated at the quantum level, where, in particular, they are singled out by the requirement of conservation of the discrete symmetries. The phenomenon is observed for the familiar pseudoclassical model of 3D P,T-invariant massive fermion system and for a new pseudoclassical model of 3D P,T-invariant system of topologically massive U(1) gauge fields.