A generalization of the Dirac equation to accelerating reference frames Available to Purchase

Using a recently developed global isometry method for treating accelerating observers, the induced tangent space transformation on flat Lorentzian R⁴ is mapped homomorphically onto a time‐dependent D^(1/2,0) ⊕ D^(0,1/2) representation of SL (2,C). The Dirac equation is shown to take on pseudoterms via this mapping. Eliminating the pseudoterms by identifying an affine connection, an exact analytic expression for the covariant derivative is found for general cases of arbitrary C² timelike observers. The transformation properties of the connection are shown to satisfy the conditions imposed by a general tetrad formalism. The specific case of the rotating observer is considered wherein the exact expression for the boosted Dirac equation is found.