Details
| Originalsprache | Englisch |
|---|---|
| Aufsatznummer | 105368 |
| Seitenumfang | 17 |
| Fachzeitschrift | Journal of geometry and physics |
| Jahrgang | 207 |
| Frühes Online-Datum | 14 Nov. 2024 |
| Publikationsstatus | Veröffentlicht - Jan. 2025 |
Abstract
We consider classical and quantum dynamics of relativistic oscillator in Minkowski space R3,1. It is shown that for a non-zero frequency parameter ω the covariant phase space of the classical Klein-Gordon oscillator is a homogeneous Kähler-Einstein manifold Z6=AdS7/U(1)=U(3,1)/U(3)×U(1). In the limit ω→0, this manifold is deformed into the covariant phase space T⁎H3 of a free relativistic particle, where H3=H+3∪H−3 is a two-sheeted hyperboloid in momentum space. Quantization of this model with ω≠0 leads to the Klein-Gordon oscillator equation which we consider in the Segal-Bargmann representation. It is shown that the general solution of this model is given by functions from the weighted Bergman space of square-integrable holomorphic (for particles) and antiholomorphic (for antiparticles) functions on the Kähler-Einstein manifold Z6. This relativistic model is Lorentz covariant, unitary and does not contain non-physical states.
ASJC Scopus Sachgebiete
- Mathematik (insg.)
- Mathematische Physik
- Physik und Astronomie (insg.)
- Allgemeine Physik und Astronomie
- Mathematik (insg.)
- Geometrie und Topologie
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in: Journal of geometry and physics, Jahrgang 207, 105368, 01.2025.
Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review
}
TY - JOUR
T1 - Klein-Gordon oscillators and Bergman spaces
AU - Popov, Alexander D.
N1 - Publisher Copyright: © 2024 The Author(s)
PY - 2025/1
Y1 - 2025/1
N2 - We consider classical and quantum dynamics of relativistic oscillator in Minkowski space R3,1. It is shown that for a non-zero frequency parameter ω the covariant phase space of the classical Klein-Gordon oscillator is a homogeneous Kähler-Einstein manifold Z6=AdS7/U(1)=U(3,1)/U(3)×U(1). In the limit ω→0, this manifold is deformed into the covariant phase space T⁎H3 of a free relativistic particle, where H3=H+3∪H−3 is a two-sheeted hyperboloid in momentum space. Quantization of this model with ω≠0 leads to the Klein-Gordon oscillator equation which we consider in the Segal-Bargmann representation. It is shown that the general solution of this model is given by functions from the weighted Bergman space of square-integrable holomorphic (for particles) and antiholomorphic (for antiparticles) functions on the Kähler-Einstein manifold Z6. This relativistic model is Lorentz covariant, unitary and does not contain non-physical states.
AB - We consider classical and quantum dynamics of relativistic oscillator in Minkowski space R3,1. It is shown that for a non-zero frequency parameter ω the covariant phase space of the classical Klein-Gordon oscillator is a homogeneous Kähler-Einstein manifold Z6=AdS7/U(1)=U(3,1)/U(3)×U(1). In the limit ω→0, this manifold is deformed into the covariant phase space T⁎H3 of a free relativistic particle, where H3=H+3∪H−3 is a two-sheeted hyperboloid in momentum space. Quantization of this model with ω≠0 leads to the Klein-Gordon oscillator equation which we consider in the Segal-Bargmann representation. It is shown that the general solution of this model is given by functions from the weighted Bergman space of square-integrable holomorphic (for particles) and antiholomorphic (for antiparticles) functions on the Kähler-Einstein manifold Z6. This relativistic model is Lorentz covariant, unitary and does not contain non-physical states.
KW - Bergman spaces
KW - Quantum relativistic oscillator
KW - Segal-Bargmann representations
UR - http://www.scopus.com/inward/record.url?scp=85209248289&partnerID=8YFLogxK
U2 - 10.48550/arXiv.2405.14349
DO - 10.48550/arXiv.2405.14349
M3 - Article
AN - SCOPUS:85209248289
VL - 207
JO - Journal of geometry and physics
JF - Journal of geometry and physics
SN - 0393-0440
M1 - 105368
ER -