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Covariant Quantization of "Massive" Spin-3/2 Fields in the de Sitter Space

By M. V. Takook, A. Azizi and E. Babaian

Abstract

We present a covariant quantization of the free "massive" spin-3/2 fields in four-dimensional de Sitter space-time based on analyticity in the complexified pseudo-Riemannian manifold. The field equation is obtained as an eigenvalue equation of the Casimir operator of the de Sitter group. The solutions are calculated in terms of coordinate-independent de Sitter plane-waves in tube domains and the null curvature limit is discussed. We give the group theoretical content of the field equation. The Wightman two-point function $S^{i \bar j}_{\alpha\alpha'}(x,x')$ is calculated. We introduce the spinor-vector field operator $\Psi_\alpha(f)$ and the Hilbert space structure. A coordinate-independent formula for the field operator $\Psi_\alpha(x)$ is also presented.Comment: 24 pages, accepted for publication in Eur. Phys. J.

Topics: General Relativity and Quantum Cosmology, Mathematical Physics
Publisher: 'Springer Science and Business Media LLC'
Year: 2012
DOI identifier: 10.1140/epjc/s10052-012-2026-x
OAI identifier: oai:arXiv.org:1206.1997

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