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

TL;DR

This paper explores conformal invariance for scalar particles in curved spacetime, deriving new Hamiltonians and equations of motion that account for gravitational effects like the Lense-Thirring effect.

Contribution

It introduces new exact Foldy-Wouthuysen Hamiltonians for scalar particles in general static and rotating spacetimes, highlighting conformal invariance in quantum mechanics.

Findings

Conformal invariance conserves Hamiltonian and wave function in the FW representation.

Derived high-precision formulas for scalar particles in various spacetime metrics.

Established classical limits of quantum equations match classical equations.

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.