Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2001-08-09
Phys.Lett. A291 (2001) 197-202
Physics
High Energy Physics
High Energy Physics - Theory
14 pages, 3figures
Scientific paper
10.1016/S0375-9601(01)00745-9
The spectrum of the Hermitian Hamiltonian ${1\over2}p^2+{1\over2}m^2x^2+gx^4$ ($g>0$), which describes the quantum anharmonic oscillator, is real and positive. The non-Hermitian quantum-mechanical Hamiltonian $H={1\over2}p^2+{1 \over2}m^2x^2-gx^4$, where the coupling constant $g$ is real and positive, is ${\cal PT}$-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 ${\cal PT}$-symmetric $-g\phi^4$ quantum field theory for all dimensions $0\leq D<3$ but is not present in the conventional Hermitian $g\phi^4$ field theory.
Bender Carl M.
Boettcher Stefan
Jones Hugh F.
Meisinger Peter
Simsek Mehmet
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