Gauss’ Law and string-localized quantum field theory

Abstract

The quantum Gauss Law as an interacting field equation is a prominent feature of QED with eminent impact on its algebraic and superselection structure and the properties of its charged particles. Because it entails the possibility of "measurement of charges at a distance", it is well-known to be in conflict with locality of charged fields [1,9]. We show how a new approach to QED advocated in [15,19,20,13] that avoids indefinite metric and ghosts, can achieve Gauss' Law. We explain why this is not at variance with recent results in [5].Dedicated to Detlev Buchholz on the occasion of his 75th birthday

Symplectic reduction of Yang-Mills theory with boundaries: from superselection sectors to edge modes, and back

“…and that ψ is a composite, generally nonlocal, 27 gauge invariant field (similar equations hold for ψ). E.g.…”

“…As proven in section 5.8, this is e.g. the interpretation embraced by the "edge 27 Spatially local dressings exist in special circumstances where the gauge symmetry is "non-substantial" [52]. 28 See [3, Sect.9] for a generalization of the notion of dressing to the case of non-Abelian connections, which relates this construction to the Vilkovisky-DeWitt geometric effective action.…”

“…where the last equation is a rewriting of (27). Now, decompose E = E Coul into its SdW-radiative ( rad ) and SdW-Coulombic (Dγ) componets, that is (E…”

“…See also:[23,24] as well as[25]. Moreover, for recent results on a residual gauge-fixing dependence of QED in the presence of (asymptotic) boundaries and flux superselection, see[26] (and also[27]). At present it is unclear how these recent results square with the classical treatment presented here 12.…”

Asymptotic charges, large gauge transformations and inequivalence of different gauges in external current QED

“…For relations between the Aharonov-Bohm effect and the Gauss Law at the level of the algebra we refer to [SDH14]. An interesting discussion of the Gauss Law and the flux of the electromagnetic field in the context of axial gauges was recently given in [BCRV19,MRS19]. Finally, we refer to [DDMS10] and references therein for the complementary case of the Dirac field in an external electromagnetic field and its sensitivity to the choice of gauge.…”