Abstract
We propose a novel description for the Higgs mechanism by which a gauge boson acquires the mass. We do not assume spontaneous breakdown of gauge symmetry signaled by a non-vanishing vacuum expectation value of the scalar field. In fact, we give a manifestly gauge-invariant description of the Higgs mechanism in the operator level, which does not rely on spontaneous symmetry breaking. This enables us to discuss the confinement-Higgs complementarity from a new perspective. The "Abelian" dominance in quark confinement of the Yang-Mills theory is understood as a consequence of the gauge-invariant Higgs phenomenon for the relevant Yang-Mills-Higgs model.
Highlights
The Brout-Englert-Higgs mechanism or Higgs phenomenon for short is one of the most well-known mechanisms by which gauge bosons [1] acquire their masses [2,3,4]
Such spontaneous symmetry breaking (SSB) of the original gauge symmetry is caused by a non-vanishing vacuum expectation value (VEV) φ = 0 of a scalar field φ governed by a given potential V (φ)
We show that a gauge boson can acquire the mass in a gauge-invariant way without assuming spontaneous breakdown of gauge symmetry which is signaled by the non-vanishing VEV of the scalar field
Summary
The Brout-Englert-Higgs mechanism or Higgs phenomenon for short is one of the most well-known mechanisms by which gauge bosons [1] acquire their masses [2,3,4]. The Higgs mechanism is understood in such a way that the spontaneous symmetry breaking (SSB) generates mass for a gauge boson: The original gauge group G is spontaneously broken down to a subgroup H by choosing a specific vacuum as the physical state from all the possible degenerate ground states (the lowest energy states) Such SSB of the original gauge symmetry is caused by a non-vanishing vacuum expectation value (VEV) φ = 0 of a scalar field φ governed by a given potential V (φ). We show that a gauge boson can acquire the mass in a gauge-invariant way without assuming spontaneous breakdown of gauge symmetry which is signaled by the non-vanishing VEV of the scalar field. The gauge-invariant description of the Higgs mechanism can shed new light on the complementarity between confinement phase and Higgs phase [17]
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