De Sitter Space is important in a lot of theory like QFT QED and others, So what are it's physical caracteristics ?
De-Sitter space-time is the maximally symmetric vacuum solution of Einstein's equations in general relativity with a positive cosmological constant. In (3+1) dimension, it is a cosmological model of the physical universe.
posted an answer to this question at https://www.quora.com/How-can-an-electron-be-in-a-superposition-state-but-change-when-being-observed/answer/Bill-Bray-6
There are two types of Sitter space, often used in physics.
The first is Sitter's space. It is in fact a 4-dimensional space with positve curvature maximally symmetrical of the other [-, +, +, +] sign. He generalizes the concept of a 4-dimensional sphere.
I will quote Jean Pierre Luminet's blog, translated into English, for a better understanding of the concept:
"De Sitter's space-time is an exact solution of the equations of ordinary general relativity discovered as early as 1917, empty of matter but which includes a repulsive force called the cosmological constant, of positive value, if we now change the sign of the constant the repulsion force becomes attractive and the model is transformed into an anti-Sitter space-time, which acquires a hyperbolic (that is, a negative curvature) spatial geometry and, although it is infinite has a well-defined "edge." To represent this edge, we use Poincaré's representation of the hyperbolic disk which, by means of a conformal transformation preserving the angles but not the distances, brings infinity to finite distance. The Dutch artist Mauritz Cornelius Escher has created a famous series of prints entitled Circle Limits in which he uses the representation of Poincaré "
Link: https://blogs.futura-sciences.com/luminet/tag/de-sitter/
The other space of sitter is its opposite, also called anti space of Sitter. This is the negative-curvature analog of the Sitter space. To be more precise, it is the vacuum solution to the Einstein field equation with a negative cosmological constant. To be even more precise, it is the Lorentzian analogue of n-dimensional hyperbolic space. It is provided with maximum symmetry and is a Lorentzian variety with constant negative scalar curvature.
But that is not the most important. Sitter's anti-space is actually more about Sitter's space, simply because it is often used as part of the ADS / CFT correspondence, itself used in string theory and theory. holographic.
I quote again Jean Pierre Luminet, same source, which I translate into English:
"For the anti-Sitter space-time in dimension 5, denoted AdS5, the edge is of dimension 4 and, locally around each point, resembles the Poincaré-Minkowski space, which is precisely the space model - flat time used in non-gravitational physics This means that a black hole in the Sitter 5D anti-space-time is strictly equivalent to a particle and radiation field existing in the 4D flat-space-time of the This last description uses well-known and controlled quantum field theories, analogous to the Yang-Mills fields used for example in quantum chromodynamics (which is the theory of strong interaction). five spatial dimensions of the anti-Sitter space-time we must add five S5 sphere-shaped compactional spatial dimensions, in order to treat the problem within the framework of the ten-dimensional standard string theory. "
And concerning the ADS / CFT correspondence, I quote simply Wikipedia:
In theoretical physics, Sitter's anti-Sitter / conformal field theory correspondence, hence its abbreviation in AdS / CFT correspondence, is a conjecture linking two types of theories. Conformal field theories (CFTs) occupy one side of the correspondence, they are quantum field theories that include similar theories to Yang-Mills that describe elementary particles, and on the other hand, anti-Sitter spaces ( AdS) are quantum gravity theories, formulated in terms of string theory or M theory. Correspondence is also sometimes called Maldacena duality or gauge / gravity duality.
Duality represents a major advance in the understanding of string theory and quantum gravity1 because it provides a non-perturbative formulation of string theory with certain boundary conditions and because it is the most successful of the holographic principle, a concept of quantum gravity originally proposed by Gerard 't Hooft then improved and put forth by Leonard Susskind. "
I hope that has been a great help to you, and I would be happy to answer other questions as well.
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