Buchholz D, Ciolli F, Ruzzi G, Vasselli E. The universal algebra of the electromagnetic field III. Static charges and emergence of
gauge fields.
Lett Math Phys 2022;
112:27. [PMID:
35400800 PMCID:
PMC8938395 DOI:
10.1007/s11005-022-01515-4]
[Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 11/05/2021] [Revised: 02/08/2022] [Accepted: 02/09/2022] [Indexed: 06/14/2023]
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.
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