Action with acceleration II: Euclide Hamiltonian and Jordan blocks
The Euclidean action with acceleration has been analyzed in Ref. 1, and referred to henceforth as Paper 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 and 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. When it is not pseudo-Hermitian, the Hamiltonian is shown to be a direct sum of Jordan blocks.
Quantum mechanics , Quantum systems with finite Hilbert space , Linear algebra|Economics
Baaquie, Belal E. (2013). Action with acceleration II: Euclide Hamiltonian and Jordan blocks. International Journal of Modern Physics, 28 (27).
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