2009
DOI: 10.1063/1.3116164
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Quantum mechanics of Proca fields

Abstract: We construct the most general physically admissible positive-definite inner product on the space of Proca fields. Up to a trivial scaling this defines a five-parameter family of Lorentz invariant inner products that we use to construct a genuine Hilbert space for the quantum mechanics of Proca fields. If we identify the generator of time-translations with the Hamiltonian, we obtain a unitary quantum system that describes first-quantized Proca fields and does not involve the conventional restriction to the posi… Show more

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Cited by 31 publications
(40 citation statements)
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References 85 publications
(211 reference statements)
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“…The application of pseudo-Hermitian QM in dealing with the Hilbert space problem in relativistic QM and quantum cosmology [150,151,161,179,114,238], and the removal of ghosts in certain quantum field theories [35,119] relies on the construction of an appropriate (positive-definite) inner product on the space of solutions of the relevant field equation.…”
Section: Relativistic Qm Quantum Cosmology and Qftmentioning
confidence: 99%
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“…The application of pseudo-Hermitian QM in dealing with the Hilbert space problem in relativistic QM and quantum cosmology [150,151,161,179,114,238], and the removal of ghosts in certain quantum field theories [35,119] relies on the construction of an appropriate (positive-definite) inner product on the space of solutions of the relevant field equation.…”
Section: Relativistic Qm Quantum Cosmology and Qftmentioning
confidence: 99%
“…The application of this construction for Klein-Gordon [161,179] and Proca [238] fields yields explicit expressions for the corresponding relativistic position operators and localized states, a problem that has been a subject of ongoing research since the 1940's [193,188]. A natural consequence of these developments is the construction of a set of genuine relativistic coherent states for Klein-Gordon fields interacting with a constant magnetic field [180].…”
mentioning
confidence: 99%
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“…This method appears to be very powerful, so such models become very popular (see, for example, [18]- [37]). …”
Section: Algebraic Theory With Maximal Massmentioning
confidence: 99%