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arXiv:quant-ph/0602161 · Annals of Physics

Quantum mechanics of Klein–Gordon fields II: Relativistic coherent states

A. Mostafazadeh, F. Zamani

Published Mar 24, 2006• 18 citations
arXivHTMLPDF
DOI
10.1016/j.aop.2006.02.008

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We use the formulation of the quantum mechanics of first quantized Klein-Gordon fields given in the first of this series of papers to study relativistic coherent states. In particular, we offer an explicit construction of coherent states for both charged and neutral (real) free Klein-Gordon fields as well as for charged fields interacting with a constant magnetic field. Our construction is free from the problems associated with charge-superselection rule that complicated the previous studies. We compute various physical quantities associated with our coherent states and present a detailed investigation of their classical (nonquantum) and nonrelativistic limits. 1

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A PHYSICAL REALIZATION OF THE GENERALIZED PT-, C-, AND CPT-SYMMETRIES AND THE POSITION OPERATOR FOR KLEIN–GORDON FIELDS

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Generalized parity [Formula: see text], time-reversal [Formula: see text], and charge-conjugation [Formula: see text] operators were initially defined in the study of the pseudo-Hermitian Hamiltonians. We construct a concrete realization of these operators for Klein–Gordon fields and show that in this realization [Formula: see text] and [Formula: see text] operators respectively correspond to the ordinary time-reversal and charge-grading operations. Furthermore, we present a complete description of the quantum mechanics of Klein–Gordon fields that is based on the construction of a Hilbert space with a relativistically invariant, positive-definite, and conserved inner product. In particular we offer a natural construction of a position operator and the corresponding localized and coherent states. The restriction of this position operator to the positive-frequency fields coincides with the Newton–Wigner operator. Our approach does not rely on the conventional restriction to positive-frequency fields. Yet it provides a consistent quantum mechanical description of Klein–Gordon fields with a genuine probabilistic interpretation.

arXiv:quant-ph/0307059•International Journal of Modern Physics A•May 10, 2006•39 citations
We use the formulation of the quantum mechanics of first quantized Klein-Gordon fields given in the first of this series of papers to study relativistic coherent states. In particular, we offer an explicit construction of coherent states for both charged and neutral (real) free Klein-Gordon fields as well as for charged fields interacting with a constant magnetic field. Our construction is free from the problems associated with charge-superselection rule that complicated the previous studies. We compute various physical quantities associated with our coherent states and present a detailed investigation of their classical (nonquantum) and nonrelativistic limits. 1
Generalized parity [Formula: see text], time-reversal [Formula: see text], and charge-conjugation [Formula: see text] operators were initially defined in the study of the pseudo-Hermitian Hamiltonians. We construct a concrete realization of these operators for Klein–Gordon fields and show that in this realization [Formula: see text] and [Formula: see text] operators respectively correspond to the ordinary time-reversal and charge-grading operations. Furthermore, we present a complete description of the quantum mechanics of Klein–Gordon fields that is based on the construction of a Hilbert space with a relativistically invariant, positive-definite, and conserved inner product. In particular we offer a natural construction of a position operator and the corresponding localized and coherent states. The restriction of this position operator to the positive-frequency fields coincides with the Newton–Wigner operator. Our approach does not rely on the conventional restriction to positive-frequency fields. Yet it provides a consistent quantum mechanical description of Klein–Gordon fields with a genuine probabilistic interpretation.