2006/07/31 by T. Garidi, J-P. Gazeau, J.-P. Gazeau +2 · 6 citations
Physics and Astronomy · #Analytic continuation #Anti-de Sitter space #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Covariant transformation #De Sitter space #De Sitter universe #Gauge theory #Massless particle #Noncommutative and Quantum Gravity Theories #Quantization (signal processing) #de Sitter invariant special relativity #gr-qc
paper · pdf · doi:10.1063/1.2841327
published as J.Math.Phys.49:032501,2008 · 33 pages, 3 figures
arxiv created 2006/07/31 · openalex publication_date 2008/03/01 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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.