Spontaneous symmetry breaking and the Goldstone theorem in non-Hermitian field theories

We demonstrate the extension to parity-time (PT)-symmetric field theories of the Goldstone theorem, confirming that the spontaneous appearance of a field vacuum expectation value via minimization of the effective potential in a non-Hermitian model is accompanied by a massless scalar boson. Laying a...

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Main Authors: Alexandre, Jean, Ellis, John, Millington, Peter, Seynaeve, Dries
Format: Article
Language:English
Published: American Physical Society 2018
Online Access:https://eprints.nottingham.ac.uk/53415/
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author Alexandre, Jean
Ellis, John
Millington, Peter
Seynaeve, Dries
author_facet Alexandre, Jean
Ellis, John
Millington, Peter
Seynaeve, Dries
author_sort Alexandre, Jean
building Nottingham Research Data Repository
collection Online Access
description We demonstrate the extension to parity-time (PT)-symmetric field theories of the Goldstone theorem, confirming that the spontaneous appearance of a field vacuum expectation value via minimization of the effective potential in a non-Hermitian model is accompanied by a massless scalar boson. Laying a basis for our analysis, we first show how the conventional quantization of the path-integral formulation of quantum field theory can be extended consistently to a non-Hermitian model by considering PT conjugation instead of Hermitian conjugation. The extension of the Goldstone theorem to a PT-symmetric field theory is made possible by the existence of a conserved current that does not, however, correspond to a symmetry of the non-Hermitian Lagrangian. In addition to extending the proof of the Goldstone theorem to a PT-symmetric theory, we exhibit a specific example in which we verify the existence of a massless boson at the tree and one-loop levels.
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spelling nottingham-534152018-08-22T15:27:50Z https://eprints.nottingham.ac.uk/53415/ Spontaneous symmetry breaking and the Goldstone theorem in non-Hermitian field theories Alexandre, Jean Ellis, John Millington, Peter Seynaeve, Dries We demonstrate the extension to parity-time (PT)-symmetric field theories of the Goldstone theorem, confirming that the spontaneous appearance of a field vacuum expectation value via minimization of the effective potential in a non-Hermitian model is accompanied by a massless scalar boson. Laying a basis for our analysis, we first show how the conventional quantization of the path-integral formulation of quantum field theory can be extended consistently to a non-Hermitian model by considering PT conjugation instead of Hermitian conjugation. The extension of the Goldstone theorem to a PT-symmetric field theory is made possible by the existence of a conserved current that does not, however, correspond to a symmetry of the non-Hermitian Lagrangian. In addition to extending the proof of the Goldstone theorem to a PT-symmetric theory, we exhibit a specific example in which we verify the existence of a massless boson at the tree and one-loop levels. American Physical Society 2018-08-01 Article PeerReviewed application/pdf en cc_by https://eprints.nottingham.ac.uk/53415/1/PhysRevD.98.045001.pdf Alexandre, Jean, Ellis, John, Millington, Peter and Seynaeve, Dries (2018) Spontaneous symmetry breaking and the Goldstone theorem in non-Hermitian field theories. Physical Review D, 98 (4). p. 5001. ISSN 2470-0010 https://journals.aps.org/prd/pdf/10.1103/PhysRevD.98.045001 10.1103/physrevd.98.045001 10.1103/physrevd.98.045001 10.1103/physrevd.98.045001
spellingShingle Alexandre, Jean
Ellis, John
Millington, Peter
Seynaeve, Dries
Spontaneous symmetry breaking and the Goldstone theorem in non-Hermitian field theories
title Spontaneous symmetry breaking and the Goldstone theorem in non-Hermitian field theories
title_full Spontaneous symmetry breaking and the Goldstone theorem in non-Hermitian field theories
title_fullStr Spontaneous symmetry breaking and the Goldstone theorem in non-Hermitian field theories
title_full_unstemmed Spontaneous symmetry breaking and the Goldstone theorem in non-Hermitian field theories
title_short Spontaneous symmetry breaking and the Goldstone theorem in non-Hermitian field theories
title_sort spontaneous symmetry breaking and the goldstone theorem in non-hermitian field theories
url https://eprints.nottingham.ac.uk/53415/
https://eprints.nottingham.ac.uk/53415/
https://eprints.nottingham.ac.uk/53415/