Dual oscillators and Quantum Pendulums: spectrum and correlators
arXiv:hep-th/0703052 · doi:10.1103/PhysRevD.76.025003
Abstract
We outline the nonlinear transformation in the path integral representation for partition function of O(N) symmetric oscillator systems bringing their duality to certain one-dimensional oscillators with unstable potential shapes. This duality transformation realizes the equivalence between spectra of a Hermitian and a non-Hermitian Hamiltonians. It is exploited to calculate exactly the spectra of quantum rotators . The zero-temperature limit is considered and the dual representation of n-point correlators of coordinate operators is obtained.
12 pages, substantial changes: calculation of correlators added