Gauge invariance and the Englert-Brout-Higgs mechanism in non-Hermitian field theories

Abstract

We discuss $\mathcal{P}\mathcal{T}$-symmetric Abelian gauge field theories, as well as their extension to the Englert-Brout-Higgs mechanism for generating a mass for a vector boson. Gauge invariance is not straightforward, and we discuss the different related problems, as well as a solution which consists in coupling the gauge field to a current that is not conserved. Non-Hermiticity then necessarily precludes the Lorenz gauge condition but nevertheless allows for a consistent formulation of the theory. We therefore generalise the Englert-Brout-Higgs mechanism to $\mathcal{P}\mathcal{T}$-symmetric field theories, opening the way to constructing non-Hermitian extensions of the Standard Model and new scenarios for particle model-building.

arXiv comment19 pages

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• 't Hooft-Polyakov monopoles in non-Hermitian quantum field theory
• Massive gauge particles versus Goldstone bosons in non-Hermitian non-Abelian gauge theory
• Field Theory of Dissipative Systems with Gapped Momentum States
• Transition Probabilities in the Two-Level Quantum System with PT-Symmetric Non-Hermitian Hamiltonians
• PT symmetric fermionic field theories with axions: Renormalization and dynamical mass generation
• Causality, unitarity, and indefinite metric in Maxwell-Chern-Simons extensions
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• The probability flow in the Stock market and Spontaneous symmetry breaking in Quantum Finance
• Complex BPS solitons with real energies from duality
• The connection between multiple prices of an Option at a given time with single prices defined at different times: The concept of weak-value in quantum finance
• Poincaré symmetries and representations in pseudo-Hermitian quantum field theory
• The phase diagram and vortex properties of PT-symmetric non-Hermitian two-component superfluid
• Non-Hermitian Yukawa interactions of fermions with axions: potential microscopic origin and dynamical mass generation
• Renormalisation group flows connecting a $4-\epsilon$ dimensional Hermitian field theory to a $\mathcal{P}\mathcal{T}$-symmetric theory for a fermion coupled to an axion
• Symmetry properties of non-Hermitian PT-symmetric quantum field theories
• Non-Hermiticity: a new paradigm for model building in particle physics
• Wilsonian approach to the interaction ${\varphi }^2(i\varphi {)}^{\epsilon }$
• Decay of the Higgs boson $h\to {\tau }^{-}{\tau }^{+}\to {\pi }^{-}{\nu }_{\tau }{\pi }^{+}{\bar{\nu }}_{\tau }$ for a non-Hermitian Yukawa interaction
• The counting of Nambu-Goldstone bosons in a non-Hermitian field theory
• Complex topological soliton with real energy in particle physics
• On the multiplicity of the martingale condition: Spontaneous symmetry breaking in Quantum Finance
• Oscillators with imaginary coupling: spectral functions in quantum mechanics and quantum field theory
• $\mathcal{P}\mathcal{T}-$Symmetric Two-Level Open Quantum Systems: Information Theoretic Facets
• On the probability flow in the Stock market I: The Black-Scholes case
• Oscillation probabilities for a PT-symmetric non-Hermitian two-state system