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

• URL: http://arxiv.org/abs/2012.12355v2
• Date: Sun, 7 Nov 2021 12:09:59 GMT
• Title: What can we learn from the conformal noninvariance of the Klein-Gordon equation?
• Authors: F. Hammad, P. Sadeghi, N. Fleury, A. Leblanc
• Abstract summary: 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.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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