The universal algebra of the electromagnetic field III. Static charges and emergence of gauge fields

Abstract

A universal C*-algebra of gauge invariant operators is presented, describing the electromagnetic field as well as operations creating pairs of static electric charges having opposite signs. Making use of Gauss' law, it is shown that the string-localized operators, which necessarily connect the charges, induce outer automorphisms of the algebra of the electromagnetic field. Thus they carry additional degrees of freedom which cannot be created by the field. It reveals the fact that gauge invariant operators encode information about the presence of non-observable gauge fields underlying the theory. Using the Gupta-Bleuler formalism, concrete implementations of the outer automorphisms by exponential functions of the gauge fields are presented. These fields also appear in unitary operators inducing the time translations in the resulting representations of the universal algebra.

14 pages, no figures

References in corpus (4)

• Infraparticle quantum fields and the formation of photon clouds
• $C^{\ast }$-algebraic approach to interacting quantum field theory: Inclusion of Fermi fields
• The universal C*-algebra of the electromagnetic field II. Topological charges and spacelike linear fields
• The universal algebra of the electromagnetic field III. Static charges and emergence of gauge fields

Cited by in corpus (3)

• The universal algebra of the electromagnetic field III. Static charges and emergence of gauge fields
• On the Thermodynamics of the q-Particles
• Twisting factors and fixed-time models in quantum field theory