A Generalization of Mackey's Theory of Induced Representations

TL;DR

This paper extends Mackey's theory to a broader class of Krein-space induced representations, including those relevant for gauge fields in the Standard Model, establishing key theorems in this context.

Contribution

It generalizes Mackey's theory to Krein-isometric representations, covering important physical models like gauge fields in the Standard Model.

Findings

Validates subgroup and Kronecker product theorems for the extended class

Includes representations in Krein-Hilbert and Fock-Krein spaces for gauge fields

Applicable to massless gauge free fields in the Standard Model

Abstract

In this work we extend the Mackey's theory of induced unitary representations on a wide class of Krein-isometric induced representations in Krein spaces. The subgroup theorem and the Kronecker product theorem are shown to be valid for the induced representations of this class. Among the class of representations which are subsumed by this extension there are all the representations acting in the single particle Krein-Hilbert space and in Fock-Krein spaces of the mass less gauge free fields underling the Standard Model in the local gauge BRST formalutaion, e. g. of the electromagnetic potential field.