Regular Article - Theoretical Physics
Gauge-independent Brout–Englert–Higgs mechanism and Yang–Mills theory with a gauge-invariant gluon mass term
Department of Physics, Graduate School of Science, Chiba University, Chiba, 263-8522, Japan
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Accepted: 5 July 2018
Published online: 17 July 2018
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.
© The Author(s), 2018