Abstract:
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 MM, this parameter MM being interpreted as a new physical constant (“fundamental mass”). Expansion with respect to unitary representations of the group of motions of the Lobachevskii pp 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 MM. In this representation local gauge transformations of the matter and vector fields are defined. Because the theory contains the “fundamental mass” MM, 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)0(4) invariance of the model. In the low-energy approximation (M→∞M→∞) the theory is equivalent to the standard theory.
Citation:
V. G. Kadyshevskii, D. V. Fursaev, “On a generalization of the gauge principle at high energies”, TMF, 83:2 (1990), 197–206; Theoret. and Math. Phys., 83:2 (1990), 474–481
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