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.

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

References in corpus (51)

• Generalization of the Proca Action
• Is the quantum state real? An extended review of $\psi$-ontology theorems
• Question of quantum equivalence between Jordan frame and Einstein frame
• Equivalence of the Einstein and Jordan frames
• Probing gravity by holding atoms for 20 seconds
• Physical non-equivalence of the Jordan and Einstein frames
• Some aspects of the cosmological conformal equivalence between ``Jordan Frame'' and ``Einstein Frame''
• Relativistic quantum mechanics and the Bohmian interpretation
• Hydrodynamic representation of the Klein-Gordon-Einstein equations in the weak field limit: I. General formalism and perturbations analysis
• Conformal equivalence in classical gravity: the example of "veiled" General Relativity
• A question mark on the equivalence of Einstein and Jordan frames
• The phase of a quantum mechanical particle in curved spacetime
• Weyl vs. Conformal
• Neutrino Interferometry In Curved Spacetime
• The covariant, time-dependent Aharonov-Bohm Effect
• Frame (In)equivalence in Quantum Field Theory and Cosmology
• The spatial relation between the event horizon and trapping horizon
• Mass dependence of the gravitationally-induced wave-function phase
• Quantum Equivalence of $f(R)$ Gravity and Scalar-tensor Theories in the Jordan and Einstein Frames
• Noether charge and black hole entropy in teleparallel gravity
• Matter waves in a gravitational field: An index of refraction for massive particles in general relativity
• About Some Problems Raised by the Relativistic Form of De-Broglie--Bohm Theory of Pilot Wave
• Affine quantisation of the Brans-Dicke theory: Smooth bouncing and the equivalence between the Einstein and Jordan frames
• Hawking-Hayward quasi-local energy under conformal transformations
• Conformal Invariance and Electrodynamics: Applications and General Formalism
• Conformally rescaled spacetimes and Hawking radiation
• Equivalence of cosmological observables in conformally related scalar tensor theories
• The horizon-entropy increase law for causal and quasi-local horizons and conformal field redefinitions
• Stokes' theorem, gauge symmetry and the time-dependent Aharonov-Bohm effect
• Revisiting the conformal invariance of Maxwell's equations in curved spacetime
• On the equivalence of Jordan and Einstein frames in scale-invariant gravity
• More on the conformal mapping of quasi-local masses: The Hawking-Hayward case
• Black holes and wormholes subject to conformal mappings
• Conformal mapping of the Misner-Sharp mass from gravitational collapse
• Conformal Killing horizons and their thermodynamics
• A fresh look at the influence of gravity on the quantum Hall effect
• Revisiting black holes and wormholes under Weyl transformations
• Klein-Gordon equation in curved space-time
• Wave packet treatment of neutrino flavor oscillations in various spacetimes
• Landau levels in a gravitational field: The Schwarzschild spacetime case
• Prospects for testing the inverse-square law and gravitomagnetism using quantum interference
• Landau levels in a gravitational field: The Levi-Civita and Kerr spacetimes case
• Equivalence of Einstein and Jordan frames in quantized cosmological models
• Revisiting wormhole energy conditions in Riemann-Cartan spacetimes and under Weyl transformations
• Gravitationally induced quantum transitions
• Quantum Phase Shift in Chern-Simons Modified Gravity
• A simple superconductor quantum interference device for testing gravity
• Compatibility of symmetric quantization with general covariance in the Dirac equation and spin connections
• Black hole mechanics and thermodynamics in the light of Weyl transformations
• More on spacetime thermodynamics in the light of Weyl transformations
• Modified Friedmann equations via conformal Bohm -- De Broglie gravity