Goldstone bosons and the Englert-Brout-Higgs mechanism in non-Hermitian theories
Goldstone bosons and the Englert-Brout-Higgs mechanism in non-Hermitian theories
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非厄米理论中的戈德斯通玻色子和恩格勒特-布劳特-希格斯机制
DOI：
10.1103/physrevd.99.045006
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发表时间：
2018
影响因子：
5
通讯作者：
P. Mannheim
中科院分区：
文献类型：
--
作者：
P. Mannheim
在最近的工作亚历山大，埃利斯，米林顿和Seynaeve已经扩大了戈德斯通定理的非厄米哈密顿拥有一个离散的反线性对称，如$PT $。他们把讨论限制在那些反线性对称的实现上，在这些实现中，所有的哈密顿能量本征值都是真实的。在这里，我们将讨论扩展到其他两个可能的实现与反线性对称，即能量在复共轭对或约旦块哈密顿是不可对角化的。特别是，我们表明，在某些情况下，它是可能的戈德斯通玻色子模式本身是一个零范数的状态，约旦块哈密顿的特点。虽然我们讨论的是与亚历山大等人相同的模型，但我们的处理方式却大不相同，尽管他们的主要结论，即在非厄米特的情况下可以有戈德斯通玻色子，仍然保持不变。在他们的论文中，亚历山大等人提出了一种变分方法，其中表面项起着显式的作用，从而表明人们必须使用这种方法才能建立非厄米特情况下的戈德斯通定理。然而，通过采取某些领域，他们采取了厄米实际上要么是反厄米，或者是这样的相似变换，我们表明，我们然后能够获得一个戈德斯通玻色子使用一个完全标准的变分过程。由于我们使用的是标准的变分方法，我们可以很容易地通过引入规范玻色子将我们的分析扩展到连续的局部对称性。我们表明，当我们这样做的规范玻色子获得一个非零质量的希格斯机制在所有实现的反线性对称性，除了一个戈德斯通玻色子本身具有零规范，在这种情况下，尽管连续的局部对称性已自发破缺，规范玻色子保持无质量。
In recent work Alexandre, Ellis, Millington and Seynaeve have extended the Goldstone theorem to non-Hermitian Hamiltonians that possess a discrete antilinear symmetry such as $PT$. They restricted their discussion to those realizations of antilinear symmetry in which all the energy eigenvalues of the Hamiltonian are real. Here we extend the discussion to the two other realizations possible with antilinear symmetry, namely energies in complex conjugate pairs or Jordan-block Hamiltonians that are not diagonalizable at all. In particular, we show that under certain circumstances it is possible for the Goldstone boson mode itself to be one of the zero-norm states that are characteristic of Jordan-block Hamiltonians. While we discuss the same model as Alexandre et al. our treatment is quite different, though their main conclusion that one can have Goldstone bosons in the non-Hermitian case remains intact. In their paper Alexandre et al. presented a variational procedure for the action in which the surface term played an explicit role, to thus suggest that one has to use such a procedure in order to establish the Goldstone theorem in the non-Hermitian case. However, by taking certain fields that they took to be Hermitian to actually either be anti-Hermitian or be made so by a similarity transformation, we show that we are then able to obtain a Goldstone boson using a completely standard variational procedure. Since we use a standard variational procedure we can readily extend our analysis to a continuous local symmetry by introducing a gauge boson. We show that when we do this the gauge boson acquires a non-zero mass by the 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.
非厄米场论中的自发对称破缺和戈德斯通定理
影响因子：
5
作者：
Alexandre J
通讯作者：
Alexandre J