We present the fundamental solutions for the spin-1/2 fields propagating in spacetimes with power type expansion/contraction and the fundamental solution of the Cauchy problem for the Dirac equation. The derivation of these fundamental solutions is based on formulas for the solutions to the generalized Euler-Poisson-Darboux equation, which are obtained by the integral transform approach.
Yagdjian, Karen, and Anahit Galstian. 2021. “Fundamental Solutions for the Dirac Equation in Curved Spacetime and Generalized Euler-Poisson-Darboux Equation.” Journal of Differential Equations 300 (November): 80–117. https://doi.org/10.1016/j.jde.2021.07.033.
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Journal of Differential Equations