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

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 $S_{\alpha {\alpha }^{\prime }}^{i\bar{j}}(x,x^{\prime })$ 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.

24 pages, accepted for publication in Eur. Phys. J. C

References in corpus (3)

• "Massless" vector field in de Sitter Universe
• Conformally Invariant "Massless" Spin-2 Field in de Sitter Universe
• Gravitino Propagator in anti de Sitter space

Cited by in corpus (5)

• Super-gauge Field in de Sitter Universe
• Quantum Yang-Mills theory in de Sitter ambient space formalism
• Scalar spinor fields interaction in de Sitter ambient space formalism
• "Massless'' Spin-$\frac{3}{2}$ Fields in the de Sitter Space
• De Sitter scalar-spinor interaction in Minkowski limit