Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
1999-04-08
Class.Quant.Grav. 17 (2000) 1415-1434
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
20 pages, appear in class. quantum grav
Scientific paper
10.1088/0264-9381/17/6/307
We present in this paper a fully covariant quantization of the minimally-coupled massless field on de Sitter space. We thus obtain a formalism free of any infrared (e.g logarithmic) divergence. Our method is based on a rigorous group theoretical approach combined with a suitable adaptation (Krein spaces) of the Wightman-G\"{a}rding axiomatic for massless fields (Gupta-Bleuler scheme). We make explicit the correspondence between unitary irreducible representations of the de Sitter group and the field theory on de Sitter space-time. The minimally-coupled massless field is associated with a representation which is the lowest term of the discrete series of unitary representations of the de Sitter group. In spite of the presence of negative norm modes in the theory, no negative energy can be measured: expressions as $\le n_{k_1}n_{k_2}...|T_{00}|n_{k_1}n_{k_2}...\re$ are always positive.
Gazeau Jean Pierre
Renaud Jacques
Vahid Takook Mohammad
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