The Maxwell Group and the Quantum Theory of Particles in Classical Homogeneous Electromagnetic Fields

Abstract Covariant solutions of the Dirac (and Klein‐Gordon) equation in a homogeneous classical electromagnetic field are constructed. This is done using the symmetry group of the equation, the Maxwell group. These covariant solutions are obtained starting from solutions in the frame where the electromagnetic field is described by a magnetic field pointing in the 3‐direction and then using the theory of induced representations.

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