Exact PT-Symmetry Is Equivalent to Hermiticity

Details Exact PT-Symmetry Is Equivalent to Hermiticity Exact PT-Symmetry Is Equivalent to Hermiticity

2003-04-11

arxiv.org/abs/quant-ph/0304080v2

J.Phys.A36:7081-7092,2003

Physics

Quantum Physics

Few typos have been corrected and a reference updated

Scientific paper

10.1088/0305-4470/36/25/312

We show that a quantum system possessing an exact antilinear symmetry, in particular PT-symmetry, is equivalent to a quantum system having a Hermitian Hamiltonian. We construct the unitary operator relating an arbitrary non-Hermitian Hamiltonian with exact PT-symmetry to a Hermitian Hamiltonian. We apply our general results to PT-symmetry in finite-dimensions and give the explicit form of the above-mentioned unitary operator and Hermitian Hamiltonian in two dimensions. Our findings lead to the conjecture that non-Hermitian CPT-symmetric field theories are equivalent to certain nonlocal Hermitian field theories.

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