Current Operators in Quantum Field Theory and Sum Rules in Deep Inelastic Scattering

TL;DR

This paper demonstrates that canonical current operators in quantum field theory violate Lorentz invariance due to Schwinger terms, challenging the validity of sum rules in deep inelastic scattering.

Contribution

It reveals the nonexistence of canonical current operators for spinor fields and questions the foundation of sum rules in deep inelastic scattering.

Findings

Canonical current operators violate Lorentz invariance.

Sum rules in deep inelastic scattering are not substantiated.

Nonexistence of canonical current operators for spinor fields.

Abstract

It is shown that in the general case the canonical construction of the current operators in quantum field theory does not render a bona fide vector field since Lorentz invariance is violated by Schwinger terms. We argue that the nonexistence of the canonical current operators for spinor fields follows from a very simple algebraic consideration. As a result, the well-known sum rules in deep inelastic scattering are not substantiated.