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No-ghost theorem for the fourth-order derivative Pais-Uhlenbeck oscillator model

Bender, C. and Mannheim, P. D. (2008). No-ghost theorem for the fourth-order derivative Pais-Uhlenbeck oscillator model. Physical Review Letters, 100(11), e110402. doi: 10.1103/PhysRevLett.100.110402

Abstract

A new realization of the fourth-order derivative Pais-Uhlenbeck oscillator is constructed. This realization possesses no states of negative norm and has a real energy spectrum that is bounded below. The key to this construction is the recognition that in this realization the Hamiltonian is not Dirac Hermitian. However, the Hamiltonian is symmetric under combined space reflection P and time reversal T. The Hilbert space that is appropriate for this PT-symmetric Hamiltonian is identified and it is found to have a positive-definite inner product. Furthermore, the time-evolution operator is unitary.

Publication Type: Article
Additional Information: Copyright American Physical Society, 2008
Subjects: Q Science > QC Physics
Departments: School of Mathematics, Computer Science & Engineering > Mathematics
URI: http://openaccess.city.ac.uk/id/eprint/13276
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