dorsal/arxiv
View SchemaA Physical Realization of the Generalized PT-, C-, and CPT-Symmetries and the Position Operator for Klein-Gordon Fields
| Authors | Ali Mostafazadeh |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0307059 |
| URL | https://arxiv.org/abs/quant-ph/0307059 |
| DOI | 10.1142/S0217751X06028813 |
| Journal | Int. J. Mod. Phys. A 21, 2553-2572 (2006) |
Abstract
Generalized parity (P), time-reversal (T), and charge-conjugation (C)operators were initially definedin 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 PT and C 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.
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"abstract": "Generalized parity (P), time-reversal (T), and charge-conjugation\n(C)operators were initially definedin the study of the pseudo-Hermitian\nHamiltonians. We construct a concrete realization of these operators for\nKlein-Gordon fields and show that in this realization PT and C operators\nrespectively correspond to the ordinary time-reversal and charge-grading\noperations. Furthermore, we present a complete description of the quantum\nmechanics of Klein-Gordon fields that is based on the construction of a Hilbert\nspace with a relativistically invariant, positive-definite, and conserved inner\nproduct. In particular we offer a natural construction of a position operator\nand the corresponding localized and coherent states. The restriction of this\nposition operator to the positive-frequency fields coincides with the\nNewton-Wigner operator. Our approach does not rely on the conventional\nrestriction to positive-frequency fields. Yet it provides a consistent quantum\nmechanical description of Klein-Gordon fields with a genuine probabilistic\ninterpretation.",
"arxiv_id": "quant-ph/0307059",
"authors": [
"Ali Mostafazadeh"
],
"categories": [
"quant-ph",
"hep-th",
"math-ph",
"math.MP"
],
"doi": "10.1142/S0217751X06028813",
"journal_ref": "Int. J. Mod. Phys. A 21, 2553-2572 (2006)",
"title": "A Physical Realization of the Generalized PT-, C-, and CPT-Symmetries and the Position Operator for Klein-Gordon Fields",
"url": "https://arxiv.org/abs/quant-ph/0307059"
},
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