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 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

scholarly journals Gravitational turbulent instability of anti-de Sitter space

2012 ◽  
Vol 29 (19) ◽  
pp. 194002 ◽  
Author(s):  
Óscar J C Dias ◽  
Gary T Horowitz ◽  
Jorge E Santos
Keyword(s):  
De Sitter Space ◽  
De Sitter

scholarly journals Open quantum entanglement: a study of two atomic system in static patch of de Sitter space

2020 ◽  
Vol 80 (8) ◽  
Author(s):  
Samim Akhtar ◽  
Sayantan Choudhury ◽  
Satyaki Chowdhury ◽  
Debopam Goswami ◽  
Sudhakar Panda ◽  
...  
Keyword(s):  
Scalar Field ◽  
Density Matrix ◽  
Master Equation ◽  
Quantum Entanglement ◽  
De Sitter Space ◽  
Thermal Bath ◽  
Massless Scalar Field ◽  
De Sitter ◽  
Open Quantum ◽  
Non Locality

Abstract In this work, our prime objective is to study non-locality and long range effect of two body correlation using quantum entanglement from various information theoretic measure in the static patch of de Sitter space using a two body Open Quantum System (OQS). The OQS is described by a system of two entangled atoms, surrounded by a thermal bath, which is modelled by a massless probe scalar field. Firstly, we partially trace over the bath field and construct the Gorini Kossakowski Sudarshan Lindblad (GSKL) master equation, which describes the time evolution of the reduced subsystem density matrix. This GSKL master equation is characterized by two components, these are-Spin chain interaction Hamiltonian and the Lindbladian. To fix the form of both of them, we compute the Wightman functions for probe massless scalar field. Using this result alongwith the large time equilibrium behaviour we obtain the analytical solution for reduced density matrix. Further using this solution we evaluate various entanglement measures, namely Von-Neumann entropy, R$$e'$$e′nyi entropy, logarithmic negativity, entanglement of formation, concurrence and quantum discord for the two atomic subsystem on the static patch of De-Sitter space. Finally, we have studied violation of Bell-CHSH inequality, which is the key ingredient to study non-locality in primordial cosmology.

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