"Massive" vector field in de Sitter space

TL;DR

This paper develops a covariant quantization method for massive vector fields in de Sitter space, emphasizing analyticity and group representation correspondence, extending previous work on scalar and spinor fields.

Contribution

It introduces a covariant quantization framework for massive vector fields in de Sitter space using analyticity and group representations, advancing the field's theoretical foundation.

Findings

Established a covariant quantization scheme for vector fields in de Sitter space.

Defined the Hilbert space structure and field operators for the theory.

Extended previous scalar and spinor field quantization methods to vector fields.

Abstract

We present in this paper a covariant quantization of the ``massive'' vector field on de Sitter (dS) space based on analyticity in the complexified pseudo-Riemanian 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-G\"arding axiomatic for vector field on dS space. The Hilbert space structure and the unsmeared field operators $K_\alpha(x)$ are also defined. This work is in the direct continuation of previous one concerning the scalar and the spinor cases.