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“Massive” vector field in de Sitter space. (English) Zbl 0978.81062
J. Math. Phys. 41, No. 9, 5920-5933 (2000); comment ibid. 43, No. 12, 6379 (2002).
Summary: We present in this paper a covariant quantization of the “massive” vector field on de Sitter space based on analyticity in the complexified pseudo-Riemannian manifold. The correspondence between unitary irreducible representations of the de Sitter group and the field theory on de Sitter space-time is essential in our approach. We introduce the Wightman two-point function for the case of generalized free vector fields on de Sitter space. This function satisfies the conditions of (a) positiveness, (b) locality, (c) covariance, (d) normal analyticity, (e) transversality and (f) divergencelessness. The Hilbert space structure and the unsmeared field operators \(K_\alpha(x)\) are also defined. This work is in the direct continuation of previous ones concerning the scalar and spinor cases.

MSC:
81T20 Quantum field theory on curved space or space-time backgrounds
83C47 Methods of quantum field theory in general relativity and gravitational theory
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