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Bound states of non-Hermitian quantum field theories. (English) Zbl 0983.81045
Summary: The spectrum of the Hermitian Hamiltonian \({1/over 2}p^2+{1/over 2}m^2x^2+gx^4\) \((g>0)\), which describes the quantum anharmonic oscillator, is real and positive. The non-Hermitian quantum-mechanical Hamiltonian \(H={1/over 2}p^2+{1/over 2}m^2x^2-gx^4\), where the coupling constant \(g\) is real and positive, is PT-symmetric. As a consequence, the spectrum of \(H\) is known to be real and positive as well. Here, it is shown that there is a significant difference between these two theories: when \(g\) is sufficiently small, the latter Hamiltonian exhibits a two-particle bound state while the former does not. The bound state persists in the corresponding non-Hermitian PT-symmetric \(-g\phi^4\) quantum field theory for all dimensions \(0\leqslant D<3\) but is not present in the conventional Hermitian \(g\phi^4\) field theory.

81T10 Model quantum field theories
81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
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