Integration of the Dirac equation with an external electromagnetic field is explored in the framework of the method of separation of variables and of the method of noncommutative integration. We have found a new type of solutions that are not obtained by separation of variables for several external electromagnetic fields. We have considered an example of crossed electric and magnetic fields of a special type for which the Dirac equation admits a nonlocal symmetry operator.

We propose a method for calculating vacuum means of the scalar field energy-momentum tensor on Lie groups and homogeneous spaces. We use the generalized harmonic analysis based on the method of coadjoint representation orbits.

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