Field theory equations

In this book, the equations of relativistic field theory are examined and, in particular, the covariance and symmetry properties of the Dirac-Maxwell and Dirac-Yang-Mills equations are considered. Several new sets of equations, called the model equations of field theory, are dealt with. These systems of equations reproduce the basic properties of standard systems of field theory equations. At the same time, the model equations exhibit a number of differences from the standard equations of field theory and, in particular, they have a new internal symmetry with respect to the pseudo-unitary (or symplectic, or spinor) group. Development of the concept of local pseudo-unitary (symplectic, spinor) symmetry of the model equations of field theory leads to momentous consequences. In certain sections of the book, the mathematical tools of Clifford and Atyah-Kahler algebras are applied.