Abstract
We extend gauge symmetry of Abelian gauge field to incorporate quantum gauge degrees of freedom. We twice apply the Harada--Tsutsui gauge recovery procedure to gauge-fixed theories. First, starting from the Faddeev--Popov path integral in the Landau gauge, we recover the gauge symmetry by introducing an additional field as an extended gauge degree of freedom. Fixing the extended gauge symmetry by the usual Faddeev--Popov procedure, we obtain the theory of Type I gaugeon formalism. Next, applying the same procedure to the resulting gauge-fixed theory, we obtain a theory equivalent to the extended Type I gaugeon formalism.
Highlights
The standard formalism of canonically quantized gauge theories [1,2,3,4,5] does not consider quantum-level gauge transformations
Starting with the Faddeev–Popov path integral in the Landau gauge, we extend the gauge freedom by twice applying the Harada–Tsutsui gauge recovery procedure [32]
The real scalar fields θ and χ introduced as extended gauge degrees of freedom play the roles of gaugeon fields Y+ and Y−
Summary
The standard formalism of canonically quantized gauge theories [1,2,3,4,5] does not consider quantum-level gauge transformations. The Lagrangian of the Abelian gauge field Aμ in Type I theory [6, 17] is given by. The corresponding parameter a of the tree level photon propagator (1.1) is given by a = 2α1α2 This theory extends the Type I gaugeon formalism by setting a as quadratic in the gauge fixing parameters (cf (1.2a)). Sakoda’s theory considers the total Fock space, which embeds the Fock spaces of the both gauges of the standard formalism In this theory, the q-number gauge transformation connects the Landau gauge and non-Landau a-gauge. Different from the gaugeon formalism, the q-number transformation of Sakoda’s theory cannot arbitrarily change the gauge parameter, but allows only α = 0 and α = a.
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