2006/05/08 by Carl M. Bender, Dorje C. Brody, Jun-Hua Chen +3
Physics and Astronomy · Mathematics · #hep-th #math-ph #math.MP #quant-ph
paper · pdf · doi:10.1103/physrevd.74.025016
published as Phys.Rev.D74:025016,2006 · 19 pages, 7 figures, corrected references
arxiv created 2006/05/08 · arxiv updated 2009/12/01
In a recent paper Jones and Mateo used operator techniques to show that the non-Hermitian \cP\cT-symmetric wrong-sign quartic Hamiltonian H=\half p2-gx4 has the same spectrum as the conventional Hermitian Hamiltonian H=\half p2+4g x4-√(2g) x. Here, this equivalence is demonstrated very simply by means of differential-equation techniques and, more importantly, by means of functional-integration techniques. It is shown that the linear term in the Hermitian Hamiltonian is anomalous; that is, this linear term has no classical analog. The anomaly arises because of the broken parity symmetry of the original non-Hermitian \cP\cT-symmetric Hamiltonian. This anomaly in the Hermitian form of a \cP\cT-symmetric quartic Hamiltonian is unchanged if a harmonic term is introduced into H. When there is a harmonic term, an immediate physical consequence of the anomaly is the appearance of bound states; if there were no anomaly term, there would be no bound states. Possible extensions of this work to -ϕ4 quantum field theory in higher-dimensional space-time are discussed.