Action with Acceleration II: Euclidean Hamiltonian and Jordan Blocks

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.

References in corpus (6)

• No-ghost theorem for the fourth-order derivative Pais-Uhlenbeck oscillator model
• Exactly solvable PT-symmetric Hamiltonian having no Hermitian counterpart
• Solution to the ghost problem in fourth order derivative theories
• PT Symmetry as a Generalization of Hermiticity
• PT symmetry in relativistic quantum mechanics
• Action with Acceleration I: Euclidean Hamiltonian and Path Integral

Cited by in corpus (2)

• PT Symmetry, Non-Gaussian Path Integrals, and the Quantum Black-Scholes Equation
• Action with Acceleration I: Euclidean Hamiltonian and Path Integral