Local Operator Algebras of Charged States in Gauge Theory and Gravity

TL;DR

This paper introduces an automorphism-based method to define physical charged operators in gauge theory and gravity, avoiding the cumbersome dressing procedures and preserving algebraic structures.

Contribution

It proposes a novel automorphism approach that maps local charged operators to physical non-local operators, extending algebraic techniques to charged states in gauge theories and gravity.

Findings

Automorphism maps local to physical charged operators.

Preserves algebraic structures of local operator algebras.

Provides a framework for constructing physical states in gauge theories.

Abstract

Powerful techniques have been developed in quantum field theory that employ algebras of local operators, yet local operators cannot create physical charged states in gauge theory or physical nonzero-energy states in perturbative quantum gravity. A common method to obtain physical operators out of local ones is to dress the latter using appropriate Wilson lines. This procedure destroys locality, it must be done case by case for each charged operator in the algebra, and it rapidly becomes cumbersome, particularly in perturbative quantum gravity. In this paper we present an alternative approach to the definition of physical charged operators: we define an automorphism that maps an algebra of local charged operators into a (non-local) algebra of physical charged operators. The automorphism is described by a formally unitary intertwiner mapping the exact BRS operator associated to the gauge symmetry into its quadratic part. The existence of an automorphism between local operators and the physical ones, describing charged states, allows to retain many of the results derived in local operator algebras and extend them to the physical-but-nonlocal algebra of charged operators as we discuss in some simple applications of our construction. We also discuss a formal construction of physical states and possible obstructions to it.