An exact solution to the equation of classical motion of a charged particle in external uniform time-dependent electric and magnetic fields is obtained in two forms by two methods. An exact solution of a more general initial-value problem is found as well.

The exact solution to the Cauchy problem for a generalized “linear” vectorial Fokker-Planck equation is found by using the disentangling techniques of Feynman and algebraic (operational) methods.

Some multidimensional generalizations of the Fokker-Planck equation used by R. Friedrich and J. Peinke for the description of a turbulent cascade as a stochastic process of Markovian type, are considered. The exact solutions of the Cauchy problems for these equations are found with the operator methods.

It is demonstrated that in the framework of quantum field theory with non-Euclidean momentum space there exist several different equally acceptable expressions for the Dirac wave operator, which depend parametrically on the fundamental massM. As a result there appears the necessity to consider fermion fields of different types, includingexotic fields which increase in the flat limitM→∞ as √M. The description of all fermionic fields is made along the lines accepted in the previous article of this series. The main feature of the developed approach —the locality of the theory in configuration space of five dimensions— is conserved.

The present paper is the second of a new series of our publications on quantum field theory with the fundamental mass. Here the theory of the free electromagnetic field and the Yang-Mills field is developed adequately by taking into account the non-Euclidean character of the momentum 4-space. Similarly to the scalar model this scheme allows a specific local formulation in the five-dimensional configuration space. It is remarkable that the symmetry of the theory with respect to gauge transformations within this formulation looks like a broken local gauge symmetry in five dimensions, the breaking mechanism being of universal form.

For the first time I met Mag (under this name Matey was known to his relatives and friends) in 1966 in Yalta, where an International School on Theoretical Physics was held. A year later I was invited to ICTP, Trieste, where Mag had already been staying for several months. For about half a year we had intensively worked together on a three-dimensional formulation of a relativistic two-particle problem in quantum field theory (QFT). Since then, our scientific and friendly contacts had not been interrupted until his passing away.