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Massive fields of arbitrary spin in curved space-times

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Abstract

A possibility to describe massive fields of spins≧1/2 within general relativity theory without auxiliary fields and subsidiary conditions is proposed. Using the 2-component spinor calculus the Lagrangian is given for arbitrarys in an uniform manner. The related Euler-Lagrange equations are the wave equations studied by Buchdahl and Wünsch. The results are specified for fields of integer and half-integer spin: A suitable generalization of Proca's equation and Lagrangian leads to an equivalent tensor description of bosonic fields, whereas a generalization of Dirac's theory allows an equivalent description of fermionic fields by use of bispinors. AU (1)-gauge invariance of the Lagrangian is obtained by coupling to an electrogmagnetic potential. The current vector of the spin-s field is derived.

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  1. Institut für Mathematik, Pädagogische Hochschule Erfurt, Nordhäuser Straße 63, D-99089, Erfurt, Germany

    Reinhard Illge

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  1. Reinhard Illge
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Communicated by K. Gawedzki

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Illge, R. Massive fields of arbitrary spin in curved space-times. Commun.Math. Phys. 158, 433–457 (1993). https://doi.org/10.1007/BF02096798

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  • DOI: https://doi.org/10.1007/BF02096798

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