dorsal/arxiv
View SchemaStanding waves in the Lorentz-covariant world
| Authors | Y. S. Kim, Marilyn E. Noz |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0409165 |
| URL | https://arxiv.org/abs/quant-ph/0409165 |
| DOI | 10.1007/s10701-005-6410-3 |
| Journal | Found.Phys. 35 (2005) 1289-1305 |
Abstract
When Einstein formulated his special relativity, he developed his dynamics for point particles. Of course, many valiant efforts have been made to extend his relativity to rigid bodies, but this subject is forgotten in history. This is largely because of the emergence of quantum mechanics with wave-particle duality. Instead of Lorentz-boosting rigid bodies, we now boost waves and have to deal with Lorentz transformations of waves. We now have some understanding of plane waves or running waves in the covariant picture, but we do not yet have a clear picture of standing waves. In this report, we show that there is one set of standing waves which can be Lorentz-transformed while being consistent with all physical principle of quantum mechanics and relativity. It is possible to construct a representation of the Poincar\'e group using harmonic oscillator wave functions satisfying space-time boundary conditions. This set of wave functions is capable of explaining the quantum bound state for both slow and fast hadrons. In particular it can explain the quark model for hadrons at rest, and Feynman's parton model hadrons moving with a speed close to that of light.
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"abstract": "When Einstein formulated his special relativity, he developed his dynamics\nfor point particles. Of course, many valiant efforts have been made to extend\nhis relativity to rigid bodies, but this subject is forgotten in history. This\nis largely because of the emergence of quantum mechanics with wave-particle\nduality. Instead of Lorentz-boosting rigid bodies, we now boost waves and have\nto deal with Lorentz transformations of waves. We now have some understanding\nof plane waves or running waves in the covariant picture, but we do not yet\nhave a clear picture of standing waves. In this report, we show that there is\none set of standing waves which can be Lorentz-transformed while being\nconsistent with all physical principle of quantum mechanics and relativity. It\nis possible to construct a representation of the Poincar\\\u0027e group using\nharmonic oscillator wave functions satisfying space-time boundary conditions.\nThis set of wave functions is capable of explaining the quantum bound state for\nboth slow and fast hadrons. In particular it can explain the quark model for\nhadrons at rest, and Feynman\u0027s parton model hadrons moving with a speed close\nto that of light.",
"arxiv_id": "quant-ph/0409165",
"authors": [
"Y. S. Kim",
"Marilyn E. Noz"
],
"categories": [
"quant-ph",
"hep-ph",
"hep-th"
],
"doi": "10.1007/s10701-005-6410-3",
"journal_ref": "Found.Phys. 35 (2005) 1289-1305",
"title": "Standing waves in the Lorentz-covariant world",
"url": "https://arxiv.org/abs/quant-ph/0409165"
},
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