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No-Ghost Theorem for the Fourth-Order Derivative Pais-Uhlenbeck Oscillator Model
Open accessAbstract
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.
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Citations
Cites
Making sense of non-Hermitian Hamiltonians
Bender, C. M. (2007) · Reports on Progress in Physics · doi:10.1088/0034-4885/70/6/r03 · Cited by 2,984
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Cited by
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Joyce, A., Jain, B., Khoury, J., & Trodden, M. (2015) · Physics Reports · doi:10.1016/j.physrep.2014.12.002 · Cited by 1,231
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Ishak, M. (2019) · Living Reviews in Relativity · doi:10.1007/s41114-018-0017-4 · Cited by 449
Making the Case for Conformal Gravity
Mannheim, P. D. (2012) · Foundations of Physics · doi:10.1007/s10701-011-9608-6 · Cited by 326
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Metadata
- Authors
- Bender, C. M., & Mannheim, P. D.
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 2008-03-18
- Volume
- 100
- Issue
- 11
- Pages
- 110402-110402
- ISSN
- 0031-9007 (ISSN-L)
- 1079-7114
- OpenAlex
- W2071163582
- Cited by
- 341
- References
- 1
- FWCI
- 9.47
- Type
- journal article
- Language
- en
- Open access
- bronze
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- Bender, C. M., & Mannheim, P. D. (2008). No-Ghost Theorem for the Fourth-Order Derivative Pais-Uhlenbeck Oscillator Model. Physical Review Letters. https://doi.org/10.1103/physrevlett.100.110402
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