dorsal/arxiv
View SchemaFinite Quantum Kinematics of the Harmonic Oscillator
| Authors | Mohsen Shiri-Garakani, David Ritz Finkelstein |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0411203 |
| URL | https://arxiv.org/abs/quant-ph/0411203 |
Abstract
Arbitrarily small changes in the commutation relations suffice to transform the usual singular quantum theories into regular quantum theories. This process is an extension of canonical quantization that we call general quantization. Here we apply general quantization to the time-independent linear harmonic oscillator. The unstable Heisenberg group becomes the stable group SO(3). This freezes out the zero-point energy of very soft or very hard oscillators, like those responsible for the infrared or ultraviolet divergencies of usual field theories, without much changing the medium oscillators. It produces pronounced violations of equipartition and of the usual uncertainty relations for soft or hard oscillators,and interactions between the previously uncoupled excitation quanta of the oscillator, weakly attractive for medium quanta, strongly repulsive for soft or hard quanta.
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"abstract": "Arbitrarily small changes in the commutation relations suffice to transform\nthe usual singular quantum theories into regular quantum theories. This process\nis an extension of canonical quantization that we call general quantization.\nHere we apply general quantization to the time-independent linear harmonic\noscillator. The unstable Heisenberg group becomes the stable group SO(3). This\nfreezes out the zero-point energy of very soft or very hard oscillators, like\nthose responsible for the infrared or ultraviolet divergencies of usual field\ntheories, without much changing the medium oscillators. It produces pronounced\nviolations of equipartition and of the usual uncertainty relations for soft or\nhard oscillators,and interactions between the previously uncoupled excitation\nquanta of the oscillator, weakly attractive for medium quanta, strongly\nrepulsive for soft or hard quanta.",
"arxiv_id": "quant-ph/0411203",
"authors": [
"Mohsen Shiri-Garakani",
"David Ritz Finkelstein"
],
"categories": [
"quant-ph"
],
"title": "Finite Quantum Kinematics of the Harmonic Oscillator",
"url": "https://arxiv.org/abs/quant-ph/0411203"
},
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