Some remarks on the spectral functions of the Abelian Higgs Model

Abstract

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.

arXiv comment32 pages, 12 figures

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• Remarks on the Clauser-Horne-Shimony-Holt inequality in relativistic quantum field theory
• Gauge Invariant Description of the $SU(2)$ Higgs model: Ward identities and Renormalization
• Reconstructing the graviton
• Spectral Functions of Gauge Theories with Banks-Zaks Fixed Points
• Study of the renormalization of BRST invariant local composite operators in the $U(1)$ Higgs model
• On the complex structure of Yang-Mills theory
• Källén-Lehmann Spectral Representation of the Scalar SU(2) Glueball
• Effects of a quark chemical potential on the analytic structure of the gluon propagator
• The Abelian Higgs model under a gauge invariant looking glass: exploiting new Ward identities for gauge invariant operators and the Equivalence Theorem