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Register a new userWhat can we learn from the conformal noninvariance of the Klein-Gordon equation?
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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 at the nonrelativistic regime leading to the Schrodinger 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 Maxwells 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 Maxwells equations. Finally, the consequence of the noninvariance of the equation on the Aharonov-Bohm effect in curved spacetime is discussed. The issues that arise at each of these different levels are thoroughly analyzed.
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