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.

Buchholz, D., Ciolli, F., Ruzzi, G., Vasselli, E. (2022). The universal algebra of the electromagnetic field III. Static charges and emergence of gauge fields. LETTERS IN MATHEMATICAL PHYSICS, 112(2) [10.1007/s11005-022-01515-4].

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

Ciolli F.;Ruzzi G.;
2022

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.
Pubblicato
Rilevanza internazionale
Articolo
Esperti anonimi
Settore MAT/05
Settore MAT/07
English
Con Impact Factor ISI
C*-algebras
Electromagnetic field
Gauge fields
Static charges
Buchholz, D., Ciolli, F., Ruzzi, G., Vasselli, E. (2022). The universal algebra of the electromagnetic field III. Static charges and emergence of gauge fields. LETTERS IN MATHEMATICAL PHYSICS, 112(2) [10.1007/s11005-022-01515-4].
Buchholz, D; Ciolli, F; Ruzzi, G; Vasselli, E
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2108/304814
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