Classical and Quantum Dispersion Relations

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.

References in corpus (9)

• Lorentz invariance with an invariant energy scale
• Relativity in space-times with short-distance structure governed by an observer-independent (Planckian) length scale
• Photons that travel in free space slower than the speed of light
• Arrival time differences between gravitational waves and electromagnetic signals due to gravitational lensing
• Bohm's Quantum Potential as an Internal Energy
• Do electromagnetic waves always propagate along null geodesics?
• Birefringent light propagation on anisotropic cosmological backgrounds
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• New non-linear modified massless Klein--Gordon equation

Cited by in corpus (7)

• Bohm potential is real and its effects are measurable
• Propagation of light in linear and quadratic GRIN media: The Bohm potential
• Quantum particles that behave as free classical particles
• Nondiffracting gravitational waves
• Engineering two-mode squeezed vacuum-like states by using the Bohm potential
• Accelerating Airy tensor modes of cosmological gravitational waves
• On the conditions for the classicality of a quantum particle