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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.

MSC:
 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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References:
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