Aspects of Solutions of Massive Spin-3/2 Equation in Schwarzschild Space-Time
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The general massive spin-(3/2) (Rarita–Schwinger) field equation in Schwarzschild geometry, previously separated by variable separation, is further studied. The orthogonality of the solutions of the angular equations is exploited. The study of the radial equations, that are proposed in the most detailed form, is reduced to the study of four coupled differential equations. The equations are discussed and integrated near the Schwarzschild radius and for zero and large values of the radial coordinate. A covariant product of states is considered that is induced by a conserved current. It is shown the existence of states that are bound in the scalar product without implying the existence of a discrete energy spectrum.
KeywordsSchwarzschild geometry Massive spin 3/2 equations Solution Product of states
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