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

Alexandre, Jean; Ellis, John; Millington, Peter; Seynaeve, Dries

doi:10.1103/physrevd.98.045001

Cited by 62 publications

(114 citation statements)

References 38 publications

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“…So far two distinct alternative propositions have been made to overcome this issue. Alexandre, Ellis, Millington and Seynaeve proposed to apply a non-standard variational principle by keeping some non-vanishing surface terms [17,20] or, in line with the pseudo-Hermitian/PT -symmetric quantum mechanical approach [24,25,26,27], one may seek a consistent equivalent similarity transformed Hermitian action, as pursued by Mannheim and the present authors [18,19]. While some features are the same in both approaches, e.g.…”

Section: Introductionmentioning

confidence: 90%

“…At first sight such type of theories appear to be inconsistent as the two sets of equations of motion obtained by functionally varying the action I separately with respect to the fields φ i and φ * i , δI n /δφ i = 0 and δI n /δφ * i = 0, are in general incompatible when U = I. One may, however, overcome this problem by using a non-standard variational principle combined with keeping some non-vanishing surface terms [17,20] or alternatively by exploiting the fact that the content of the theory is unaltered as long as the equal time commutation relations are preserved and carry out a similarity transformation that guarantees that feature [8,18,19]. Hence, in the latter approach one seeks a Dyson map η, named this way in analogy to its quantum mechanical counterpart [28], to construct a new equivalent actionÎ…”

Section: Pseudo-hermitian Approach To Spontaneously Broken Symmetriesmentioning

confidence: 99%

“…The generalisations also include Goldstone's theorem [12,13] and the Higgs mechanism [14,15,16] [17,18,19,20]. Both of these mechanisms are governed by the continuous symmetries of the theories, global or local, respectively, that might by spontaneously broken by some vacuum states.…”

Section: Introductionmentioning

confidence: 99%

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

Fring

Taira

2020

Phys. Rev. D

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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.

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Section: Introductionmentioning

confidence: 90%

Section: Pseudo-hermitian Approach To Spontaneously Broken Symmetriesmentioning

confidence: 99%

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

Fring

Taira

2020

Phys. Rev. D

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“…The next step was to study spontaneous symmetry breaking and the Goldstone theorem [23][24][25] in a non-Hermitian, PT -symmetric quantum field theory, which was done in Ref. [26] (cf. the alternative approach of Refs.…”

Section: Introductionmentioning

confidence: 99%

Spontaneously breaking non-Abelian gauge symmetry in non-Hermitian field theories

et al. 2020

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We generalise our previous formulation of gauge-invariant PT -symmetric field theories to include models with non-Abelian symmetries and discuss the extension to such models of the Englert-Brout-Higgs-Kibble mechanism for generating masses for vector bosons. As in the Abelian case, the non-Abelian gauge fields are coupled to non-conserved currents. We present a consistent scheme for gauge fixing, demonstrating BRST invariance, and show that the particle spectrum and interactions are gauge invariant. We exhibit the masses that gauge bosons in the simplest two-doublet SU(2)×U(1) model acquire when certain scalar fields develop vacuum expectation values: they and scalar masses depend quartically on the non-Hermitian mass parameter µ. The bosonic mass spectrum differs substantially from that in a Hermitian two-doublet model. This non-Hermitian extension of the Standard Model opens a new direction for particle model-building, with distinctive predictions to be explored further.

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“…It has also been suggested that non-Hermitian quantum field theory might also have applications in fundamental physics, e.g., to neutrino physics [8][9][10], dark matter [11] Higgs decays [12] and particle mixing [13]. It has been shown that it is possible to carry over to PT -symmetric non-Hermitian theories familiar concepts from Hermitian quantum field theory such as the spontaneous breaking of global symmetries [14][15][16] and the Englert-Brout-Higgs mechanism in gauge theories [17][18][19], despite the appearance of subtleties [20,21] in the relationship between current conservation, Lagrangian symmetries and Noether's theorem [22] in PT -symmetric theories.…”

Section: Introductionmentioning

confidence: 99%

PT -symmetric non-Hermitian quantum field theories with supersymmetry

2020

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We formulate supersymmetric non-Hermitian quantum field theories with PT symmetry, starting with free chiral boson/fermion models and then including trilinear superpotential interactions. We consider models with both Dirac and Majorana fermions, analyzing them in terms of superfields and at the component level. We also discuss the relation between the equations of motion, the (non-)invariance of the Lagrangian and the (non-)conservation of the supercurrents in the two models. We exhibit a similarity transformation that maps the free-field supersymmetric PT -symmetric Dirac model to a supersymmetric Hermitian theory, but there is in general no corresponding similarity transformation for the Majorana model. In this model we find generically a mass splitting between bosons and fermions, even though its construction is explicitly supersymmetric, offering a novel non-Hermitian mechanism for soft supersymmetry breaking. 1 The appearance of supersymmetry in a PT -symmetric quantum-mechanical model was discovered in Ref. [31]. Relations between Hermitian theories and PT -symmetric non-Hermitian theories have been derived in the framework of supersymmetric quantum mechanics [32], see Refs. [33, 34] and references therein.

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

Cited by 62 publications

References 38 publications

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

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

Spontaneously breaking non-Abelian gauge symmetry in non-Hermitian field theories

PT -symmetric non-Hermitian quantum field theories with supersymmetry

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