Scalar particle in general inertial and gravitational fields and conformal invariance revisited

Abstract

The new manifestation of conformal invariance for a massless scalar particle in a Riemannian spacetime of general relativity is found. Conformal transformations conserve the Hamiltonian and wave function in the Foldy-Wouthuysen representation. Similarity of manifestations of conformal invariance for massless scalar and Dirac particles is proved. New exact Foldy-Wouthuysen Hamiltonians are derived for both massive and massless scalar particles in a general static spacetime and in a frame rotating in the Kerr field approximated by a spatially isotropic metric. The latter case covers an observer on the ground of the Earth or on a satellite and takes into account the Lense-Thirring effect. High-precision formulas are obtained for an arbitrary spacetime metric. General quantum-mechanical equations of motion are derived. Their classical limit coincides with corresponding classical equations.

5 pages, final version

References in corpus (3)

• Dirac fermions in strong gravitational fields
• Classical Limit of Relativistic Quantum Mechanical Equations in the Foldy-Wouthuysen Representation
• Hamilton Operator and the Semiclassical Limit for Scalar Particles in an Electromagnetic Field

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