Electric charge assignment in quantum field theories

TL;DR

This paper systematically constructs the electric charge operator in the Standard Model and extensions, clarifying its relation to global and gauge symmetries in quantum field theories.

Contribution

It provides a method to systematically derive the electric charge operator from any representation in the Standard Model and its extensions.

Findings

Electric charge operator can be constructed from any representation.

Method applies to Standard Model and extensions like 3-3-1, left-right symmetric, GUTs.

Clarifies the relation between global and gauge symmetries in charge assignment.

Abstract

In Field theories with simple or semi-simple unitary, local or global symmetries, the electric charge is related to a global one. This is the case also in electroweak gauge theories even before the spontaneous symmetry breaking (SSB), where these quantities are defined in order to expand the Lagrangian respecting the conservation laws after the breaking. So, the electric charge assignment within a given multiplet is done (in units of jej) considering only global symmetries, even though in general, the electric charge operator is a linear combination of the diagonal generators of the non-Abelian symmetry plus some Abelian factor. In this work we show how this operator can be systematically constructed from any representation in the Standard Model and some of its extensions as the 3-3-1, left-right symmetric and grand unified models.