Journal
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
Volume 42, Issue 13, Pages -Publisher
IOP PUBLISHING LTD
DOI: 10.1088/1751-8113/42/13/135303
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We address the problem of coupling non-Hermitian systems, treated as fundamental rather than effective theories, to the electromagnetic field. In such theories the observables are not the x and p appearing in the Hamiltonian, but quantities X and P constructed by means of the metric operator. Following the analogous procedure of gauging a global symmetry in Hermitian quantum mechanics we find that the corresponding gauge transformation in X implies minimal substitution in the form P -> P - eA(X). We discuss how the relevant matrix elements governing electromagnetic transitions may be calculated in the special case of the Swanson Hamiltonian, where the equivalent Hermitian Hamiltonian h is local, and in the more generic example of the imaginary cubic interaction, where H is local but h is not.
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