Quantum mechanics of Proca fields
Farhad Zamani,Ali Mostafazadeh +1 more
Reads0
Chats0
TLDR
In this paper, the most general physically admissible positive-definite inner product on the space of Proca fields was constructed, up to a trivial scaling, which defines a five-parameter family of Lorentz invariant inner products that were used to construct a genuine Hilbert space for the quantum mechanics of the Proca field.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 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 ...read more
Citations
More filters
Journal ArticleDOI
Pseudo-Hermitian Representation of Quantum Mechanics
TL;DR: A diagonalizable non-Hermitian Hamiltonian having a real spectrum may be used to define a unitary quantum system, if one modifies the inner product of the Hilbert space properly as mentioned in this paper.
Journal ArticleDOI
Pseudo-Hermitian Representation of Quantum Mechanics
TL;DR: A diagonalizable non-Hermitian Hamiltonian having a real spectrum can be used to define a unitary quantum system, if one modifies the inner product of the Hilbert space properly as discussed by the authors.
Journal ArticleDOI
Three-Hilbert-Space Formulation of Quantum Mechanics
TL;DR: Znojil et al. as mentioned in this paper proposed an amended, three-Hilbert space (3HS) reformulation of the same theory and showed that the double role played by H (auxiliary) may lead to confusion in the literature.
Journal ArticleDOI
Conceptual aspects of PT -symmetry and pseudo-Hermiticity: a status report
TL;DR: In this article, the authors survey some of the main conceptual developments in the study of -symmetric and pseudo-Hermitian Hamiltonian operators that have taken place during the past 10 years or so.
Book ChapterDOI
Non‐self‐adjoint operators in quantum physics: ideas, people, and trends
TL;DR: On the occasion of the centenary of the Bohr's model of atom (1) (marking, in a way, the birth of quantum theory), one should appreciate the multitude of results of the first hundred years of our study of quantum world as discussed by the authors.
References
More filters
Journal ArticleDOI
Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry
TL;DR: The condition of self-adjointness as discussed by the authors ensures that the eigenvalues of a Hamiltonian are real and bounded below, replacing this condition by the weaker condition of $\mathrm{PT}$ symmetry, one obtains new infinite classes of complex Hamiltonians whose spectra are also real and positive.
Journal ArticleDOI
On Unitary Representations of the Inhomogeneous Lorentz Group
TL;DR: The superposition principle of the wave function is defined in this article, which is the fundamental principle of quantum mechanics that the system of states forms a linear manifold, in which a unitary scalar product is defined.
Journal ArticleDOI
Complex extension of quantum mechanics
TL;DR: If PT symmetry is not spontaneously broken, it is possible to construct a previously unnoticed symmetry C of the Hamiltonian, and this work is not in conflict with conventional quantum mechanics but is rather a complex generalization of it.
Journal ArticleDOI
Pseudo-Hermiticity versus PT Symmetry: The necessary condition for the reality of the spectrum of a non-Hermitian Hamiltonian
TL;DR: In this paper, the authors introduce the notion of pseudo-hermiticity and show that every non-Hermitian Hamiltonian with a real spectrum is pseudo-HERMIAN.