Pseudo-Hermitian approach to Goldstone's theorem in non-Abelian non-Hermitian quantum field theories

Abstract

We generalise previous studies on the extension of Goldstone's theorem from Hermitian to non-Hermitian quantum field theories with Abelian symmetries to theories possessing a glocal non-Abelian symmetry. We present a detailed analysis for a non-Hermitian field theory with two complex two component scalar fields possessing a SU(2)-symmetry and indicate how our finding extend to the general case. In the PT-symmetric regime and at the standard exceptional point the Goldstone theorem is shown to apply, although different identification procedures need to be employed. At the zero exceptional points the Goldstone boson can not be identified. Comparing our approach, based on the pseudo-Hermiticity of the model, to an alternative approach that utilises surface terms to achieve compatibility for the non-Hermitian system, we find that the explicit forms of the Goldstone boson fields are different.

arXiv comment14 pages, 2 figures

References in corpus (16)

• Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry
• Pseudo-Hermitian Representation of Quantum Mechanics
• Dual PT-Symmetric Quantum Field Theories
• Dense loops, supersymmetry, and Goldstone phases in two dimensions
• Symmetries and conservation laws in non-Hermitian field theories
• Spontaneous symmetry breaking and the Goldstone theorem in non-Hermitian field theories
• PT-symmetric quantum field theory in D dimensions
• Goldstone bosons and the Englert-Brout-Higgs mechanism in non-Hermitian theories
• Non-Hermitian extension of gauge theories and implications for neutrino physics
• Goldstone bosons in different PT-regimes of non-Hermitian scalar quantum field theories
• Spontaneously Breaking Non-Abelian Gauge Symmetry in Non-Hermitian Field Theories
• Critical behavior of the PT-symmetric $i{\varphi }^3$ quantum field theory
• Foldy-Wouthuysen transformation for non-Hermitian Hamiltonians
• Decay of the Higgs boson to ${\tau }^{-}{\tau }^{+}$ and non-Hermiticity of the Yukawa interaction
• PT-Symmetric Quantum Electrodynamics and Unitarity
• The Yukawa Model in One Space - One Time Dimensions

Cited by in corpus (24)

• Discrete spacetime symmetries and particle mixing in non-Hermitian scalar quantum field theories
• $\mathcal{P}\mathcal{T}$-symmetric $-g{\phi }^4$ theory
• PT-Symmetric Non-Hermitian Quantum Field Theories with Supersymmetry
• Massive gauge particles versus Goldstone bosons in non-Hermitian non-Abelian gauge theory
• 't Hooft-Polyakov monopoles in non-Hermitian quantum field theory
• On the consistency of a non-Hermitian Yukawa interaction
• An introduction to PT-symmetric quantum mechanics -- time-dependent systems
• PT symmetric fermionic field theories with axions: Renormalization and dynamical mass generation
• Spontaneous Non-Hermiticity in Nambu-Jona-Lasinio model
• Non-Hermitian Holography
• Non-Hermitian gauge field theories and BPS limits
• Discrete spacetime symmetries, second quantization, and inner products in a non-Hermitian Dirac fermionic field theory
• IR/UV mixing from local similarity maps of scalar non-Hermitian field theories
• Complex BPS solitons with real energies from duality
• Poincaré symmetries and representations in pseudo-Hermitian quantum field theory
• Non-Hermitian Yukawa interactions of fermions with axions: potential microscopic origin and dynamical mass generation
• Schwinger-Dyson equations and mass generation for an axion theory with a PT symmetric Yukawa fermion interaction
• 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
• 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
• Complex topological soliton with real energy in particle physics
• Oscillation probabilities for a PT-symmetric non-Hermitian two-state system
• Conformal bridge transformation, $\mathcal{P}\mathcal{T}$- and super- symmetry