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Some remarks on the spectral functions of the Abelian Higgs Model
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We consider the unitary Abelian Higgs model and investigate its spectral functions at one-loop order. This analysis allows to disentangle what is physical and what is not at the level of the elementary particle propagators, in conjunction with the Nielsen identities. We highlight the role of the tadpole graphs and the gauge choices to get sensible results. We also introduce an Abelian Curci-Ferrari action coupled to a scalar field to model a massive photon which, like the non-Abelian Curci-Ferarri model, is left invariant by a modified non-nilpotent BRST symmetry. We clearly illustrate its non-unitary nature directly from the spectral function viewpoint. This provides a functional analogue of the Ojima observation in the canonical formalism: there are ghost states with nonzero norm in the BRST-invariant states of the Curci-Ferrari model.
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Cited by 2 Pith papers
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The Equivalence Theorem at work: manifestly gauge-invariant Abelian Higgs model physics
The Abelian Higgs action is rewritten with gauge-invariant FMS operators as elementary fields, and one-loop renormalizability is demonstrated via the Equivalence Theorem.
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