Parity and Fermions in Front-Form: An Unexpected Result

TL;DR

This paper investigates how parity transformations affect Weyl spinors in the front-form framework, revealing that parity does not interchange certain spinor representations and implying the need to consider evolution along both light-front directions.

Contribution

It demonstrates that parity does not interchange Weyl spinors in the front-form, challenging assumptions about degrees of freedom in front-form field theories.

Findings

Parity does not interchange (1/2,0) and (0,1/2) Weyl spinors in the front form.

Parity covariance requires evolution along both x^+ and x^- directions.

Possible no halving of degrees of freedom in front-form field theories.

Abstract

We show that under the operation of parity the {\it front-form} $(1/2,\,0)$ and $(0,\,1/2)$ Weyl spinors (massive or massless) do not get interchanged. This has the important consequence that if a front-form theory containing $(1/2,\,0)\oplus(0,\,1/2)$ representation space has to be parity covariant then one must study the evolution of a physical system not only along $x^+$ but also along the $x^-$ direction. As a result of our analysis, we find an indication that there may be no halving of the degrees of freedom in the front form of field theories.