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On quantum numbers for Rarita-Schwinger fields. (English) Zbl 1476.81038

Summary: We consider first order linear operators commuting with the operator appearing in the linearized equation of motion of Rarita-Schwinger fields which comes directly from the action. First we consider a simplified operator giving an equation equivalent to the original equation, and classify first order operators commuting with it in four dimensions. In general such operators are symmetry operators of the original operator, but we find that some of them commute with it. We extend this result in four dimensions to arbitrary dimensions and give first order commuting operators constructed of odd rank Killing-Yano and even rank closed conformal Killing-Yano tensors with additional conditions.

MSC:

81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
81R25 Spinor and twistor methods applied to problems in quantum theory
81R20 Covariant wave equations in quantum theory, relativistic quantum mechanics
81R10 Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, \(W\)-algebras and other current algebras and their representations

Software:

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References:

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