Hermitian gravity and supergravity

Physics

Scientific paper

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Field Theory (Physics), Gravitation Theory, Hermitian Polynomial, Lagrangian Equilibrium Points, Supergravity, Approximation, Vector Currents, Weak Interactions (Field Theory)

Scientific paper

It is shown that a natural connection is established between Hermitian gravity and supergravity at a classical level and in the weak-field approximation if the axial vector contribution of the matter fields to the nonsymmetric Hermitian metric tensor, as well as the vector contribution, is considered. A phenomenological Lagrangian including spin contributions is proposed and it is shown that if the source of the gravitational field is a Majorana spin-3/2 particle, then the above-mentioned connection turns out to be metric-compatible. Finally, the gauge invariance of the Lagrangian in the weak-field approximation is investigated.

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