Pure Spinor Formalism for Conformal Fermion and Conserved Currents

TL;DR

This paper develops a pure spinor formalism to construct conformal-invariant wave equations and Lagrangians for massive fermions, demonstrating invariance of the Dirac Lagrangian under conformal transformations.

Contribution

It introduces a novel pure spinor approach to formulate conformal-invariant fermion equations and Lagrangians, extending the understanding of conformal symmetry in fermionic theories.

Findings

Constructed conformal-invariant wave equation and Lagrangian for massive fermions

Proved invariance of Dirac Lagrangian under conformal transformations

Utilized pure spinor formalism and exponential factors

Abstract

Pure spinor formalism and non-integrable exponential factors are used for constructing the conformal-invariant wave equation and Lagrangian density for massive fermion. It is proved that canonical Dirac Lagrangian for massive fermion is invariant under induced projective conformal transformations.