Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2006-10-23
Phys.Rev.D74:125022,2006
Physics
High Energy Physics
High Energy Physics - Theory
LaTeX, 12 pages, no figures
Scientific paper
10.1103/PhysRevD.74.125022
It can be shown using operator techniques that the non-Hermitian $PT$-symmetric quantum mechanical Hamiltonian with a "wrong-sign" quartic potential $-gx^4$ is equivalent to a Hermitian Hamiltonian with a positive quartic potential together with a linear term. A naive derivation of the same result in the path-integral approach misses this linear term. In a recent paper by Bender et al. it was pointed out that this term was in the nature of a parity anomaly and a more careful, discretized treatment of the path integral appeared to reproduce it successfully. However, on re-examination of this derivation we find that a yet more careful treatment is necessary, keeping terms that were ignored in that paper. An alternative, much simpler derivation is given using the additional potential that has been shown to appear whenever a change of variables to curvilinear coordinates is made in a functional integral.
Jones Hugh F.
Mateo J.
Rivers Ray J.
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