QED Representation for the Net of Causal Loops

Abstract

The present work tackles the existence of local gauge symmetries in the setting of Algebraic Quantum Field Theory (AQFT). The net of causal loops, previously introduced by the authors, is a model independent construction of a covariant net of local C*-algebras on any 4-dimensional globally hyperbolic spacetime, aimed to capture some structural properties of any reasonable quantum gauge theory. In fact, representations of this net can be described by causal and covariant connection systems, and the local gauge transformations arise as maps between equivalent connection systems. The present paper completes these abstract results, realizing QED as a representation of the net of causal loops in Minkowski spacetime. More precisely, we map the quantum electromagnetic field Fμν, not free in general, into a representation of the net of causal loops and show that the corresponding connection system and local gauge transformations find a counterpart in terms of Fμν.

Some changes about notation

References in corpus (5)

• Batalin-Vilkovisky formalism in perturbative algebraic quantum field theory
• Warped Convolutions, Rieffel Deformations and the Construction of Quantum Field Theories
• Quantization of Maxwell's equations on curved backgrounds and general local covariance
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Cited by in corpus (3)

• The universal C*-algebra of the electromagnetic field
• On the Thermodynamics of the q-Particles
• Background potentials and superselection sectors