Action with Acceleration II: Euclidean Hamiltonian and Jordan Blocks
Quantum Physics
2015-06-12 v1 Mathematical Physics
math.MP
Abstract
The Euclidean action with acceleration has been analyzed in [1], hereafter cited as reference I, for its Hamiltonian and path integral. In this paper, the state space of the Hamiltonian is analyzed for the case when it is pseudo-Hermitian (equivalent to a Hermitian Hamiltonian), as well as the case when it is inequivalent. The propagator is computed using both creation/destruction operators as well as the path integral. A state space calculation of the propagator shows the crucial role played by the dual state vectors that yields a result impossible to obtain from a Hermitian Hamiltonian acting on a Hilbert space. When it is not pseudo-Hermitian, the Hamiltonian is shown to be a direct sum of Jordan blocks.
Cite
@article{arxiv.1211.7166,
title = {Action with Acceleration II: Euclidean Hamiltonian and Jordan Blocks},
author = {Belal E. Baaquie},
journal= {arXiv preprint arXiv:1211.7166},
year = {2015}
}