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Register a new userSuper-gauge Field in de Sitter Universe
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Added by
Mohammad Vahid Takook
Publication date
2015
fields
Physics
and research's language is
English
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The Gupta-Bleuler triplet for vector-spinor gauge field is presented in de Sitter ambient space formalism. The invariant space of field equation solutions is obtained with respect to an indecomposable representation of the de Sitter group. By using the general solution of the massless spin-$frac{3}{2}$ field equation, the vector-spinor quantum field operator and its corresponding Fock space is constructed. The quantum field operator can be written in terms of the vector-spinor polarization states and a quantum conformally coupled massless scalar field, which is constructed on Bunch-Davies vacuum state. The two-point function is also presented, which is de Sitter covariant and analytic.
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In the present work the massless vector field in the de Sitter (dS) space has been quantized. Massless is used here by reference to conformal invariance and propagation on the dS light-cone whereas massive refers to those dS fields which contract at zero curvature unambiguously to massive fields in Minkowski space. Due to the gauge invariance of the massless vector field, its covariant quantization requires an indecomposable representation of the de Sitter group and an indefinite metric quantization. We will work with a specific gauge fixing which leads to the simplest one among all possible related Gupta-Bleuler structures. The field operator will be defined with the help of coordinate independent de Sitter waves (the modes) which are simple to manipulate and most adapted to group theoretical matters. The physical states characterized by the divergencelessness condition will for instance be easy to identify. The whole construction is based on analyticity requirements in the complexified pseudo-Riemanian manifold for the modes and the two-point function.
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 present and describe an exact solution of Einsteins equations which represents a snapping cosmic string in a vacuum background with a cosmological constant $Lambda$. The snapping of the string generates an impulsive spherical gravitational wave which is a particular member of a known family of such waves. The global solution for all values of $Lambda$ is presented in various metric forms and interpreted geometrically. It is shown to represent the limit of a family of sandwich type N Robinson-Trautman waves. It is also derived as a limit of the C-metric with $Lambda$, in which the acceleration of the pair of black holes becomes unbounded while their masses are scaled to zero.
The construction of exact linearized solutions to the Einstein equations within the Bondi-Sachs formalism is extended to the case of linearization about de Sitter spacetime. The gravitational wave field measured by distant observers is constructed, leading to a determination of the energy measured by such observers. It is found that gravitational wave energy conservation does not normally apply to inertial observers, but that it can be formulated for a class of accelerated observers, i.e. with worldlines that are timelike but not geodesic.
The massless minimally coupled scalar field in de Sitter ambient space formalism might play a similar role to what the Higgs scalar field accomplishes within the electroweak standard model. With the introduction of a local transformation for this field, the interaction Lagrangian between the scalar field and the spinor field can be made similar to a gauge theory. In the null curvature limit, the Yukawa potential can be constructed from that Lagrangian. Finally the one-loop correction of the scalar-spinor interaction is presented, which is free of any infrared divergence.
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