Conformal symmetry, chiral fermions and semiclassical approximation

Joanna Gonera,Piotr Kosiński,Paweł Maślanka

doi:10.1016/j.physletb.2019.135111

Abstract

The explicit form of conformal generators is found which provides the extension of Poincare symmetry for massless particles of arbitrary helicity. The helicity 12 particles are considered as the particular example. The realization of conformal symmetry in the semiclassical regime of Weyl equation is obtained.

Highlights

In recent years the dynamics of chiral fermions became a field of intense research [1]-[20]
1 2 massless fermions the starting point is the Weyl equation in electromagnetic field; the latter is typically viewed as classical external one, at least in the context we are concerned here
For many applications the electromagnetic field is assumed to be weak and slowly varying which allows for the use of semiclassical approximation

Summary

Introduction

In recent years the dynamics of chiral fermions became a field of intense research [1]-[20]. This topic is interesting due to its applications, for example in exploring anomalyrelated phenomena in kinetic theory, and because its complete theoretical description requires to combine the diverse ideas concerning topology, symmetries, anomalies, Berry’s phases etc. The semiclassical action functional lacks manifest Lorentz covariance (which becomes Lorentz symmetry in the absence of external fields), in spite of the fact that it is derived from explicitly covariant Weyl equation. [11] where a modified transformation rule under Lorentz boosts has been proposed It involves O(ħ) corrections which are helicity-dependent and provide on-shell implementation of Poincare covariance on semiclassical level.

Conformally invariant dynamics

Semiclassical approximation

Conclusions