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arXiv · 2012.12355

What can we learn from the conformal noninvariance of the Klein-Gordon equation?

F. Hammad·P. Sadeghi·N. Fleury·A. Leblanc
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Abstract

It is well known that the Klein-Gordon equation in curved spacetime is conformally noninvariant, both with and without a mass term. We show that such a noninvariance provides nontrivial physical insights at different levels, first within the fully relativistic regime, then in the nonrelativistic regime leading to the Schr\"odinger equation, and then within the de Broglie-Bohm causal interpretation of quantum mechanics. The conformal noninvariance of the Klein-Gordon equation coupled to a vector potential is confronted with the conformal invariance of Maxwell's equations in the presence of a charged current. The conformal invariance of the non-minimally coupled Klein-Gordon equation to gravity is then examined in light of the conformal invariance of Maxwell's equations. Finally, the consequence of the noninvariance of the equation on the Aharonov-Bohm effect in curved spacetime is discussed.

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F. Hammad, P. Sadeghi, N. Fleury, A. Leblanc. 2020-12-22. What can we learn from the conformal noninvariance of the Klein-Gordon equation?. https://doi.org/10.1142/s0217751x21502249

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