Exact PT-symmetry is equivalent to Hermiticity

By Ali Mostafazadeh. 2003

374 citations recorded by the source corpus.

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.

Subfields: Atomic and Molecular Physics, and Optics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/fb4ef35e3bd4be2a0031e1ee2f71bf74207c5006

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In Atomic and Molecular Physics, and Optics

In Statistical and Nonlinear Physics

Citations in the corpus

Nonlinear switching and solitons in PT‐symmetric photonic systems (2015, background): “Thus, the following question naturally arises: are there any significant differences between these PT-symmetric and Hermitian systems having the same eigenvalues in nonlinear regime? To answer this question we introduce new system, described by the equation i u̇ = −[HH + F(u)]u, where HH can be cons”
Symmetry and Topology in Non-Hermitian Physics (2018, background): “[221] A.”
Nonlinear waves in PT -symmetric systems (2016, background): “Therefore, one can also consider the generalized parity operator P (Bender, Berry, and Mandilara, 2002; Mostafazadeh, 2003b, 2008), with P being an arbitrary unitary linear operator: P†P = PP† = I.”