Gauge fields and gravity

N. P. Konopleva

Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 153 (2011) no. 3, pp. 42-49

Résumé

In connection with the energy problem in the elementary particle theory, astrophysics and cosmology, the local symmetry conception in theoretical physics and its influence on the structure of the gauge field theory are under discussion here. Einsteinian General Relativity is considered as a special case of the gauge theory, when the gauge field is given by the symmetric tensor of rank two. It is shown that the symmetry group localization leads to modification of the conservation law form. In particular, in consequence of the translation group localization the energy-momentum conservation law written in usual form becomes covariant one. Within the Lagrangian formalism for infinite Lie groups (which we worked out in 1967), this conservation law is Noether's identities corresponding to her second theorem. In the case of GR, Noether identities are generated by generally covariant transformations of the space-time coordinates considered as the local translations. In the gauge field theory the problem of the gravity energy-momentum pseudotensor does not exist. Appearance of the pseudotensor-type structures points to localization of the symmetry group of the present theory. This phenomenon characterizes modifications of all conservation law forms. A new form of the conservation laws (covariant conservation laws) is given by the identities of Noether's second theorem for each particular local symmetry. These very identities make it possible to treat geometrically the interactions of elementary particles and show in which way it must be done. The dynamical constants are obtained by integration of the corresponding differential covariant conservation laws. In this process, Petrov's classification of Riemannian spaces ought to be used.

Détail

Keywords: geometry, global and local symmetries, gravity, gauge field theory, energy problem.

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