Exact Foldy-Wouthuysen transformation for spin 0 particle in curved space
Antonio Accioly, Harold Blas
TL;DR
This paper derives an exact Foldy-Wouthuysen transformation for spin-0 particles in static curved spacetimes, expanding the known transformations beyond fermions and revealing specific gravitational effects.
Contribution
It provides the first exact FWT for scalar particles in curved space, independent of coupling strength, and compares gravitational Darwin terms with fermionic cases.
Findings
Exact FWT for spin-0 particles in static spacetimes derived
Gravitational Darwin term for conformal coupling is one third of fermionic case
Transformation exists regardless of scalar-gravity coupling strength
Abstract
Up to now, the only known exact Foldy- Wouthuysen transformation (FWT) in curved space is that concerning Dirac particles coupled to static spacetime metrics. Here we construct the exact FWT related to a real spin-0 particle for the aforementioned spacetimes. This exact transformation exists independently of the value of the coupling between the scalar field and gravity. Moreover, the gravitational Darwin term written for the conformal coupling is one third of the relevant term in the fermionic case.
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