Local Operator Algebras of Charged States in Gauge Theory and Gravity

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.  Common methods to obtain physical operators destroy locality and other properties of the local algebra. In this talk, an alternative approach to the definition of physical charged operators is presented. It employs an automorphism that maps the algebra of local charged operators into a (non-local) algebra of physical charged operators while preserving some properties of local algebras. The automorphism is described by a formally unitary intertwiner, mapping the exact BRS operator associated to the gauge symmetry into its quadratic part. We apply our technique to other dressing that have been widely used in the literature and discuss a formal construction of physical states --and possible obstructions to it.