“Massless” vector field in de Sitter universe

We proceed to the quantization of the massless vector field in the de Sitter (dS) space. This work is the natural continuation of a previous article devoted to the quantization of the dS massive vector field [J. P. Gazeau and M. V. Takook, J. Math. Phys. 41, 5920 (2000); T. Garidi et al. , ibid. 43,...

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Bibliographic Details
Published in:Journal of mathematical physics 2008-03, Vol.49 (3), p.032501-032501-25
Main Authors: Garidi, T., Gazeau, J.-P., Rouhani, S., Takook, M. V.
Format: Article
Language:English
Subjects:
CONFORMAL INVARIANCE
COSMOLOGY
DE SITTER GROUP
DE SITTER SPACE
Exact sciences and technology
FIELD OPERATORS
GAUGE INVARIANCE
General Relativity and Quantum Cosmology
LIGHT CONE
M-THEORY
Mathematical methods in physics
Mathematics
Physics
PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
QUANTIZATION
QUANTUM FIELD THEORY
Quantum theory
Sciences and techniques of general use
UNIVERSE
VECTOR FIELDS
Vector space
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Summary:We proceed to the quantization of the massless vector field in the de Sitter (dS) space. This work is the natural continuation of a previous article devoted to the quantization of the dS massive vector field [J. P. Gazeau and M. V. Takook, J. Math. Phys. 41, 5920 (2000); T. Garidi et al. , ibid. 43, 6379 (2002).] The term “massless” is used by reference to conformal invariance and propagation on the dS lightcone whereas “massive” refers to those dS fields which unambiguously contract to Minkowskian massive fields at zero curvature. Due to the combined occurrences of gauge invariance and indefinite metric, the covariant quantization of the massless vector field requires an indecomposable representation of the de Sitter group. We work with the gauge fixing corresponding to the simplest Gupta–Bleuler structure. The field operator is defined with the help of coordinate-independent de Sitter waves (the modes). The latter are simple to manipulate and most adapted to group theoretical approaches. The physical states characterized by the divergencelessness condition are, for instance, easy to identify. The whole construction is based on analyticity requirements in the complexified pseudo-Riemannian manifold for the modes and the two-point function.
ISSN:0022-2488
1089-7658
DOI:10.1063/1.2841327