Quantum mechanics of Proca fields

Journal Article · Fri May 15 04:00:00 EDT 2009 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.3116164· OSTI ID:21294092

Zamani, Farhad ^[1]; Mostafazadeh, Ali ^[2]

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1. Department of Physics, Institute for Advanced Studies in Basic Sciences, Zanjan 45195-1159 (Iran, Islamic Republic of)
2. Department of Mathematics, Koc University, Rumelifeneri Yolu, Sariyer, Istanbul 34450 (Turkey)

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 positive-frequency fields. We provide a rather comprehensive analysis of this system. In particular, we examine the conserved current density responsible for the conservation of the probabilities, explore the global gauge symmetry underlying the conservation of the probabilities, obtain a probability current density, construct position, momentum, helicity, spin, and angular momentum operators, and determine the localized Proca fields. We also compute the generalized parity (P), generalized time-reversal (T), and generalized charge or chirality (C) operators for this system and offer a physical interpretation for its PT-, C-, and CPT-symmetries.

• OSTI ID: 21294092
• Journal Information: Journal of Mathematical Physics, Journal Name: Journal of Mathematical Physics Journal Issue: 5 Vol. 50; ISSN JMAPAQ; ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ANGULAR MOMENTUM OPERATORS
CHIRAL SYMMETRY
CHIRALITY
CPT THEOREM
CURRENT DENSITY
GAUGE INVARIANCE
HAMILTONIANS
HELICITY
HILBERT SPACE
LORENTZ INVARIANCE
PARITY
PROBABILITY
QUANTUM FIELD THEORY
QUANTUM MECHANICS
RELATIVISTIC RANGE
SPIN