On a generalization of the gauge principle at high energies

A model of a Euclidean gauge theory that describes a system of interacting scalar and vector fields and is based on a more general concept of the field itself in the region of high energies is constructed. A key part is played by the Lobachevskii momentum 4-space with radius of curvature $M$, this parameter $M$ being interpreted as a new physical constant (“fundamental mass”). Expansion with respect to unitary representations of the group of motions of the Lobachevskii $p$ space plays the part of Fourier transformation. After transition to the corresponding new configuration representation, the basic equations of the theory become differential–difference equations with a step of order $M$. In this representation local gauge transformations of the matter and vector fields are defined. Because the theory contains the “fundamental mass” $M$, the law of the gauge transformation of the vector field is modified significantly and appears as a combination of standard Yang–Mills transformations and gauge transformations characteristic of the theory of a vector field on a lattice. However, this last does not break the Euclidean $0(4)$ invariance of the model. In the low-energy approximation ($M\to\infty$) the theory is equivalent to the standard theory.