dorsal/arxiv
View SchemaCoupled oscillators, entangled oscillators, and Lorentz-covariant harmonic oscillators
| Authors | Y. S. Kim, Marilyn E. Noz |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0502096 |
| URL | https://arxiv.org/abs/quant-ph/0502096 |
| DOI | 10.1088/1464-4266/7/12/005 |
| Journal | J.Opt.B Quant.Semiclass.Opt. 7 (2007) S458-S467 |
Abstract
Other than scattering problems where perturbation theory is applicable, there are basically two ways to solve problems in physics. One is to reduce the problem to harmonic oscillators, and the other is to formulate the problem in terms of two-by-two matrices. If two oscillators are coupled, the problem combines both two-by-two matrices and harmonic oscillators. This method then becomes a powerful research tool to cover many different branches of physics. Indeed, the concept and methodology in one branch of physics can be translated into another through the common mathematical formalism. Coupled oscillators provide clear illustrative examples for some of the current issues in physics, including entanglement and Feynman's rest of the universe. In addition, it is noted that the present form of quantum mechanics is largely a physics of harmonic oscillators. Special relativity is the physics of the Lorentz group which can be represented by the group of two-by-two matrices commonly called $SL(2,c)$. Thus the coupled harmonic oscillators can play the role of combining quantum mechanics with special relativity. It is therefore possible to relate the current issues of physics to the Lorentz-covariant formulation of quantum mechanics.
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"abstract": "Other than scattering problems where perturbation theory is applicable, there\nare basically two ways to solve problems in physics. One is to reduce the\nproblem to harmonic oscillators, and the other is to formulate the problem in\nterms of two-by-two matrices. If two oscillators are coupled, the problem\ncombines both two-by-two matrices and harmonic oscillators. This method then\nbecomes a powerful research tool to cover many different branches of physics.\nIndeed, the concept and methodology in one branch of physics can be translated\ninto another through the common mathematical formalism. Coupled oscillators\nprovide clear illustrative examples for some of the current issues in physics,\nincluding entanglement and Feynman\u0027s rest of the universe. In addition, it is\nnoted that the present form of quantum mechanics is largely a physics of\nharmonic oscillators. Special relativity is the physics of the Lorentz group\nwhich can be represented by the group of two-by-two matrices commonly called\n$SL(2,c)$. Thus the coupled harmonic oscillators can play the role of combining\nquantum mechanics with special relativity. It is therefore possible to relate\nthe current issues of physics to the Lorentz-covariant formulation of quantum\nmechanics.",
"arxiv_id": "quant-ph/0502096",
"authors": [
"Y. S. Kim",
"Marilyn E. Noz"
],
"categories": [
"quant-ph",
"hep-ph",
"hep-th"
],
"doi": "10.1088/1464-4266/7/12/005",
"journal_ref": "J.Opt.B Quant.Semiclass.Opt. 7 (2007) S458-S467",
"title": "Coupled oscillators, entangled oscillators, and Lorentz-covariant harmonic oscillators",
"url": "https://arxiv.org/abs/quant-ph/0502096"
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