Conformally invariant wave equations on 3+2 de sitter space

2005 ◽  
pp. 523-529
Author(s):  
J. P. Gazeau ◽  
M. Hans
Keyword(s):  
Wave Equations ◽  
De Sitter Space ◽  
De Sitter ◽  
Conformally Invariant

Wave Equations in the de Sitter Space

1949 ◽  
Vol 76 (2) ◽  
pp. 296-297 ◽  
Author(s):  
Satosi Watanabe
Keyword(s):  
Wave Equations ◽  
De Sitter Space ◽  
De Sitter

scholarly journals Conformal scattering of the Maxwell-scalar field system on de Sitter space

2019 ◽  
Vol 16 (04) ◽  
pp. 743-791
Author(s):  
Grigalius Taujanskas
Keyword(s):  
Scalar Field ◽  
De Sitter Space ◽  
Decay Rates ◽  
Energy Estimates ◽  
Small Data ◽  
De Sitter ◽  
Null Infinity ◽  
Conformally Invariant ◽  
Field System ◽  
Gauge Fixing

We prove small data energy estimates of all orders of differentiability between past null infinity and future null infinity of de Sitter space for the conformally invariant Maxwell-scalar field system. Using these, we construct bounded and invertible, but nonlinear, scattering operators taking past asymptotic data to future asymptotic data. We deduce exponential decay rates for solutions with data having at least two derivatives, and for more regular solutions discover an asymptotic decoupling of the scalar field from the charge. The construction involves a carefully chosen complete gauge fixing condition which allows us to control all components of the Maxwell potential, and a nonlinear Grönwall inequality for higher-order estimates.

scholarly journals VACUUM QUANTUM EFFECT FOR PARALLEL PLATES MOVING BY UNIFORM ACCELERATION IN STATIC DE SITTER SPACE

2005 ◽  
Vol 20 (24) ◽  
pp. 5679-5688 ◽  
Author(s):  
M. R. SETARE
Keyword(s):  
Quantum Effect ◽  
Vacuum Expectation ◽  
De Sitter Space ◽  
Dirichlet Boundary Conditions ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
Parallel Plates ◽  
De Sitter ◽  
Casimir Forces ◽  
Conformally Invariant

The Casimir forces on two parallel plates moving by uniform proper acceleration in static de Sitter background due to conformally coupled massless scalar field satisfying Dirichlet boundary conditions on the plates is investigated. Static de Sitter space is conformally related to the Rindler space, as a result we can obtain vacuum expectation values of energy–momentum tensor for conformally invariant field in static de Sitter space from the corresponding Rindler counterpart by the conformal transformation.

scholarly journals QUANTUM MECHANICS AND FIELD THEORY WITH MOMENTUM DEFINED ON AN ANTI-DE SITTER SPACE

2010 ◽  
Vol 25 (26) ◽  
pp. 4889-4899
Author(s):  
MYRON BANDER
Keyword(s):  
Wave Equations ◽  
De Sitter Space ◽  
High Energy ◽  
Space Time ◽  
De Sitter ◽  
Curved Space ◽  
High Energy Behavior ◽  
Energy Behavior ◽  
Definition Of ◽  
Energy And Momentum

Relativistic dynamics with energy and momentum restricted to an anti-de Sitter space is presented. Coordinate operators conjugate to such momenta are introduced. Definition of functions of these operators, their differentiation and integration, all necessary for the development of dynamics is presented. The resulting algebra differs from the standard Heisenberg one, notably in that the space–time coordinates do not commute among each other. The resulting time variable is discrete and the limit to continuous time presents difficulties. A parallel approach, in which an overlap function, between position and momentum states, is obtained from solutions of wave equations on this curved space are also investigated. This approach, likewise, has problems in the that high energy behavior of these overlap functions precludes a space–time definition of action functionals.

scholarly journals Wave Equations in de Sitter Space

1951 ◽  
Vol 6 (6) ◽  
pp. 1013-1014
Author(s):  
K. Goto
Keyword(s):  
Wave Equations ◽  
De Sitter Space ◽  
De Sitter
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