Parity Transformation in the Front Form

TL;DR

This paper investigates the parity transformation properties of spinor fields in the front form, revealing how dynamical degrees of freedom are distributed across light-front surfaces and implications for constructing consistent quantum field theories.

Contribution

It demonstrates the necessity of studying front-form evolution along both $x^+$ and $x^-$ directions and clarifies the distribution of degrees of freedom on light-front surfaces.

Findings

Half of the dynamical degrees of freedom reside on $x^+=0$ surface.

The other half reside on $x^-=0$ surface.

Results are essential for building consistent front-form quantum field theories.

Abstract

By considering the parity-transformation properties of the $(1/2,\,0)$ and $(0,\,1/2)$ fields in the {\it front form} we find ourselves forced to study the front-form evolution both along $x^+$ and $x^-$ directions. As a by product, we find that half of the dynamical degrees of freedom of a full theory live on the $x^+=0$ surface and the other half on the $x^-=0$ surface. Elsewhere, Jacob shows how these results are required to build a satisfactory, and internally consistent, front-form quantum field theory.