Dirac equation in metric-affine gravitation theories and superpotentials |
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Authors: | Giovanni Giachetta Luigi Mangiarotti |
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Institution: | (1) Dipartimento di Matematica e Fisica, Universitá di Camerino, 62032 Camerino (MC), Italy |
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Abstract: | We consider a metric-affine gravitational framework in which the dynamical fields are the spin structures, the general linear
connections, and the Dirac fermion fields. Using a spin structure and a linear connection on the world manifold, we construct
a principal connection on the spinor bundle. By applying general ideas concerning the conservation laws in the Lagrangian
approach to field theory, we examine the corresponding conserved currents. The main result is that the currents associated
with infinitesimal vertical (internal) transformations of the covariance group are shown to vanish identically. It follows
that to every vector field on the world manifold there corresponds a well-defined current, the stress-energymomentum of the
fields. It turns out that the fermion fields do not contribute at all to the superpotential terms. Actually the expression
we get for the superpotential generalizes the well-known expression obtained by Komar. |
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Keywords: | |
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