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PT-symmetry and its spontaneous breakdown explained by anti-linearity

Stefan Weigert
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Abstract

The impact of an anti-unitary symmetry on the spectrum of non-hermitean operators is studied. Wigner's normal form of an anti-unitary operator is shown to account for the spectral properties of non-hermitean, PT-symmetric Hamiltonians. Both the occurrence of single real or complex conjugate pairs of eigenvalues follows from this theory. The corresponding energy eigenstates span either one- or two-dimensional irreducible representations of the symmetry PT. In this framework, the concept of a spontaneously broken PT-symmetry is not needed.

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Stefan Weigert. 2002-09-06. PT-symmetry and its spontaneous breakdown explained by anti-linearity. https://doi.org/10.1088/1464-4266%2F5%2F3%2F380

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