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arXiv 2109.08714hep-thhep-ph
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Goldstone和Englert-Brout-Higgs机制对非厄米理论的推广

Extension of the Goldstone and the Englert-Brout-Higgs mechanisms to non-Hermitian theories

Philip D. Mannheim

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12 pages. Prepared for the Proceedings of Analytic and Algebraic Methods in Physics AAMP XVIII Virtual Conference, September 2021. Also presented at Virtual Pseudo-Hermitian Hamiltonians in Quantum Physics Conference, September 2021
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摘要：

我们讨论的戈德斯通和Englert-Brout-Higgs机制的扩展到非厄米哈密顿具有反线性PT对称。我们研究了一个模型，由于亚历山大，埃利斯，米林顿和Seynaeve和表明，对于连续的全球对称性的自发击穿，我们得到一个无质量的戈德斯通玻色子在所有三个反线性对称实现：本征值真实，本征值在复共轭对，和本征值真实，但本征向量不完整。在最后一种情况下，我们表明，它是可能的戈德斯通玻色子模式是一个零范数状态。对于连续局域对称性的破缺，规范玻色子在所有反线性对称性的实现中通过恩格尔-布劳特-希格斯机制获得非零质量，除了戈德斯通玻色子本身具有零范数的情况，在这种情况下，尽管连续局域对称性已经自发破缺，规范玻色子仍然没有质量。

英文摘要：

We discuss the extension of the Goldstone and Englert-Brout-Higgs mechanisms to non-Hermitian Hamiltonians that possess an antilinear PT symmetry. We study a model due to Alexandre, Ellis, Millington and Seynaeve and show that for the spontaneous breakdown of a continuous global symmetry we obtain a massless Goldstone boson in all three of the antilinear symmetry realizations: eigenvalues real, eigenvalues in complex conjugate pairs, and eigenvalues real but eigenvectors incomplete. In this last case we show that it is possible for the Goldstone boson mode to be a zero-norm state. For the breakdown of a continuous local symmetry the gauge boson acquires a non-zero mass by the Englert-Brout-Higgs mechanism in all realizations of the antilinear symmetry, except the one where the Goldstone boson itself has zero norm, in which case, and despite the fact that the continuous local symmetry has been spontaneously broken, the gauge boson remains massless.

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