Stress - energy - momentum conservation law in gauge gravitation theory

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Abstract
Building on the first variational formula of the calculus of variations, one can derive the energy - momentum conservation law from the condition that the Lie derivatives of gravitation Lagrangians along vector fields of infinitesimal covariant transformations are equal to zero. The goal is to construct these vector fields. In gauge gravitation theory, a difficulty arises because of fermion fields. Covariant transformations fail to preserve the Dirac spin structure on a world manifold X, which is associated with a certain tetrad field h. We introduce the universal Dirac spin structure such that, given a tetrad field , the restriction of S to h(X) is isomorphic to . The canonical lift of vector fields on X onto S is constructed. We discover the corresponding stress - energy - momentum conservation law where the conserved energy - momentum flow is reduced to the generalized Komar superpotential.