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.Comment: 5 pages, final versio
