Abstract
For the Yang–Mills theory coupled to a single scalar field in the fundamental representation of the gauge group, we present a gauge-independent description of the Brout–Englert–Higgs mechanism by which massless gauge bosons acquire their mass. The new description should be compared with the conventional gauge-dependent description relying on the spontaneous gauge symmetry breaking due to a choice of the non-vanishing vacuum expectation value of the scalar field. In this paper we focus our consideration on the fundamental scalar field which extends the previous work done for the Yang–Mills theory with an adjoint scalar field. Moreover, we show that the Yang–Mills theory with a gauge-invariant mass term is obtained from the corresponding gauge-scalar model when the radial degree of freedom (length) of the scalar field is fixed. The result obtained in this paper is regarded as a continuum realization of the Fradkin–Shenker continuity and Osterwalder–Seiler theorem for the complementarity between Higgs regime and Confinement regime which was given in the gauge-invariant framework of the lattice gauge theory. Moreover, we discuss how confinement is investigated through the gauge-independent Brout–Englert–Higgs mechanism by starting with the complementary gauge-scalar model.
Highlights
In previous papers [1,2] we have proposed a gauge-independent description of the Brout–Englert–Higgs (BEH) or Higgs mechanism [3,4,5,6] which is defined to be a mechanism for massless gauge bosons to acquire their mass
A e-mail: kondok@faculty.chiba-u.jp associated with the spontaneous breaking of the gauge symmetry. This description requires a non-vanishing vacuum expectation value of the scalar field, 0|φ(x)|0 = v, which is clearly gauge dependent and impossible to be realized without fixing the gauge due to the Elitzur theorem [10,11]
The massive vector mode Wμ will rapidly fall off in the distance and it is identified with the short-distance mode
Summary
In previous papers [1,2] we have proposed a gauge-independent description of the Brout–Englert–Higgs (BEH) or Higgs mechanism [3,4,5,6] which is defined to be a mechanism for massless gauge bosons to acquire their mass. The massive Yang–Mills theory obtained in this way can be efficient for understanding the confining decoupling solution in the Landau gauge which was confirmed by the numerical simulations on the lattice [66,67,68,69,70] and was examined in the analytical approach [71,72,73,74,75,76,77,78,79], see e.g. the proceedings [80,81] for the related works This enables one to provide a novel explanation for the Cornwall claim that the gluon mass can be dynamically generated in the gauge-invariant way without spontaneous symmetry breaking.
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