Gauging non-Hermitian Hamiltonians

Details Gauging non-Hermitian Hamiltonians Gauging non-Hermitian Hamiltonians

2008-11-03

arxiv.org/abs/0811.0305v2

Physics

Quantum Physics

The mimimal substitution rule given in v1 was incorrect. The corrected version appears in Eq. (21) of v2, and the necessary ch

Scientific paper

10.1088/1751-8113/42/13/135303

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 $\bs{x}$ and $\bs{p}$ appearing in the Hamiltonian, but quantities $\bs{X}$ and $\bs{P}$ 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 $\bs{X}$ implies minimal substitution in the form $\bs{P}\to \bs{P} - e\bs{A}(\bs{X})$. 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.

Affiliated with

Also associated with

No associations

Rating

Gauging non-Hermitian Hamiltonians does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Gauging non-Hermitian Hamiltonians, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Gauging non-Hermitian Hamiltonians will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-233992