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Register a new userQuantum Linear Gravity in de Sitter Universe On Gupta-Bleuler vacuum state
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Added by
Mohammad Vahid Takook
Publication date
2012
fields
Physics
and research's language is
English
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Application of Krein space quantization to the linear gravity in de Sitter space-time have constructed on Gupta-Bleuler vacuum state, resulting in removal of infrared divergence and preserving de Sitter covariant. By pursuing this path, the non uniqueness of vacuum expectation value of the product of field operators in curved space-time disappears as well. Then the vacuum expectation value of the product of field operators can be defined properly and uniquely.
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In de Sitter ambient space formalism, the linear gravity can be written in terms of a minimally coupled scalar field and a polarization tensor. In this formalism, the massless minimally coupled scalar field can be quantized on Bunch-Davies vacuum state, that preserves the de Sitter invariance, the analyticity and removes the infrared divergence. The de Sitter quantum linear gravity is then constructed on Bunch-Davies vacuum state, which is also covariant, analytic and free of any infrared divergences. We will conclude that the unique Bunch-Davies vacuum state can be used adequately to constructing the quantum field theory in de Sitter universe.
We give in this paper an explicit construction of the covariant quantization of the rank-two massless tensor field on de Sitter space (linear covariant quantum gravity on a de Sitter background). The main ingredient of the construction is an indecomposable representation of de Sitter group. We here make the choice of a specific simple gauge fixing. We show that our gauge fixing eliminates any infrared divergence in the two-point function for the traceless part of this field. But it is not possible to do the same for the pure trace part (conformal sector). We describe the related Krein space structure and covariant field operators. This work is in the continuation of our previous ones concerning the massless minimally coupled scalar fields and the massive tensor field on de Sitter.
We study the free massive scalar field in de Sitter spacetime with static charts. In particular, we find positive-frequency modes for the Bunch-Davies vacuum state natural to the static charts as superpositions of the well-known positive-frequency modes in the conformally-flat chart. We discuss in detail how these modes are defined globally in the two static charts and the region in their future. The global structure of these solutions leads to the well-known description of the Bunch-Davies vacuum state as an entangled state. Our results are expected to be useful not only for studying the thermal properties in the vacuum fluctuations in de Sitter spacetime but also for understanding the nonlocal properties of the vacuum state.
By making use of the background field method, the one-loop quantization for Euclidean Einstein-Weyl quadratic gravity model on the de Sitter universe is investigated. Using generalized zeta function regularization, the on-shell and off-shell one-loop effective actions are explicitly obtained and one-loop renormalizability, as well as the corresponding one-loop renormalization group equations, are discussed. The so called critical gravity is also considered.
Previous studies of the vacuum polarization on de Sitter have demonstrated that there is a simple, noncovariant representation of it in which the physics is transparent. There is also a cumbersome, covariant representation in which the physics is obscure. Despite being unwieldy, the latter form has a powerful appeal for those who are concerned about de Sitter invariance. We show that nothing is lost by employing the simple, noncovariant representation because there is a closed form procedure for converting its structure functions to those of the covariant representation. We also present a vastly improved technique for reading off the noncovariant structure functions from the primitive diagrams. And we discuss the issue of representing the vacuum polarization for a general metric background.
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