Classical and Quantum Dispersion Relations

• URL: http://arxiv.org/abs/2003.13559v2
• Date: Thu, 4 Feb 2021 12:50:41 GMT
• Title: Classical and Quantum Dispersion Relations
• Authors: Sergio A. Hojman and Felipe A. Asenjo
• Abstract summary: In general, classical and quantum dispersion relations are different due to the presence of the Bohm potential. Explicit examples are given for covariant scalar, vectorial and tensorial fields in flat and curved spacetimes.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: It is showed that, in general, classical and quantum dispersion relations are different due to the presence of the Bohm potential. There are exact particular solutions of the quantum (wave) theory which obey the classical dispersion relation, but they differ in the general case. The dispersion relations may also coincide when additional assumptions are made, such as WKB or eikonal approximations, for instance. This general result also holds for non--quantum wave equations derived from classical counterparts, such as in ray and wave optics, for instance. Explicit examples are given for covariant scalar, vectorial and tensorial fields in flat and curved spacetimes.

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