2001/08/09 by Carl M. Bender, Stefan Boettcher, H. F. Jones +2
Physics and Astronomy · #hep-th
paper · pdf · doi:10.1016/s0375-9601(01)00745-9
published as Phys.Lett. A291 (2001) 197-202 · 14 pages, 3figures
arxiv created 2001/08/09 · arxiv updated 2009/11/30
The spectrum of the Hermitian Hamiltonian 1\over2p2+1\over2m2x2+gx4 (g>0), which describes the quantum anharmonic oscillator, is real and positive. The non-Hermitian quantum-mechanical Hamiltonian H=1\over2p2+1 \over2m2x2-gx4, 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 -gϕ4 quantum field theory for all dimensions 0≤ D<3 but is not present in the conventional Hermitian gϕ4 field theory.