Year: 2009
Type: preprint
Abstract: A new proof is given for why the non-Hermitian, PT-Invariant cubic oscillator with imaginary coupling has real eigenvalues. The proof consists of two steps. In the first step, it is shown that for many PT-Invariant Hamiltonians, one can define corresponding Hermitian Hamiltonians that have the same eigenvalues when quantized using indefinite metric. The second step is to show that the indefinite-metric eigenvalues of the Hermitian cubic oscillator are real since the norms of its eigenstates do not vanish. The correspondence between PT-Invariant Hamiltonians and indefinite-metric Hermitian Hamiltonians is further discussed as a way to determine vacuum stability for certain supersymmetric gauge theories.
Source: arXiv (Cornell University)
Author: Chapman, Scott
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1629910899