TL;DR
This paper explores the gravitational interactions of spin-1/2 particles, deriving transformations for Dirac particles in static spacetimes and analyzing relativistic limits, highlighting ambiguities in the transformations.
Contribution
It constructs exact Foldy-Wouthuysen and Cini-Touschek transformations for Dirac particles in static spacetimes and discusses the non-uniqueness of these transformations.
Findings
Derived exact transformations for Dirac particles in static spacetime
Analyzed quasi-relativistic and ultra-relativistic limits of fermions
Identified ambiguities in the Foldy-Wouthuysen transformation
Abstract
We discuss some aspects of the gravitational interaction of the relativistic quantum particles with spin 1/2. The exact Foldy-Wouthuysen transformation is constructed for the Dirac particle coupled to the static spacetime metric. The quasi-relativistic limit of the theory is then analyzed. Using the analogous method, we obtain the exact Cini-Touschek transformation and discuss the ultra-relativistic limit of the fermion theory. We show that the Foldy-Wouthuysen transformation is not uniquely defined, and the corresponding ambiguity is deeply rooted in the relativistic quantum theory.
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