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

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 Schrödinger 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.

Length reduced, typos corrected, references added, main results emphasized. Accepted in IJMPA

References in corpus (16)

• Is the quantum state real? An extended review of $\psi$-ontology theorems
• Equivalence of the Einstein and Jordan frames
• Physical non-equivalence of the Jordan and Einstein frames
• The spatial relation between the event horizon and trapping horizon
• Noether charge and black hole entropy in teleparallel gravity
• Equivalence of cosmological observables in conformally related scalar tensor theories
• More on the conformal mapping of quasi-local masses: The Hawking-Hayward case
• Conformal mapping of the Misner-Sharp mass from gravitational collapse
• A fresh look at the influence of gravity on the quantum Hall effect
• Wave packet treatment of neutrino flavor oscillations in various spacetimes
• Landau levels in a gravitational field: The Levi-Civita and Kerr spacetimes case
• Revisiting wormhole energy conditions in Riemann-Cartan spacetimes and under Weyl transformations
• Equivalence of Einstein and Jordan frames in quantized cosmological models
• Quantum Phase Shift in Chern-Simons Modified Gravity
• A simple superconductor quantum interference device for testing gravity
• More on spacetime thermodynamics in the light of Weyl transformations