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arXiv · 1805.06380

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

Jean Alexandre·John Ellis·Peter Millington·Dries Seynaeve
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Abstract

We demonstrate the extension to PT-symmetric field theories of the Goldstone theorem, confirming that the spontaneous appearance of a field vacuum expectation value via minimisation 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 quantisation 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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Jean Alexandre, John Ellis, Peter Millington, Dries Seynaeve. 2018-05-16. Spontaneous symmetry breaking and the Goldstone theorem in non-Hermitian field theories. https://doi.org/10.1103/physrevd.98.045001

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