De Sitter space as an arena for doubly special relativity

By Jerzy Kowalski-Glikman. 2002

147 citations recorded by the source corpus.

Abstract We show that Doubly Special Relativity (DSR) can be viewed as a theory with energy–momentum space being the four-dimensional de Sitter space. Different formulations (bases) of the DSR theory considered so far can be therefore understood as different coordinate systems on this space. The emerging geometrical picture makes it possible to understand the universality of the non-commutative structure of space–time of doubly special relativity. Moreover, it suggests how to construct the most natural DSR basis, which turns out to be the bicrossproduct basis.

Subfields: Applied Mathematics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/9987f74078f01c50dfc09629bb27db2ef4d65d2e

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Giovanni Amelino-Camelia
2. Lee Smolin
3. L. Freidel
4. Jerzy Kowalski-Glikman
5. R. Gurau
6. Sabine Hossenfelder

In Statistical and Nonlinear Physics

1. Giovanni Amelino-Camelia
2. Stefano Liberati
3. Jerzy Kowalski-Glikman
4. Lee Smolin
5. L. Freidel
6. Matt Visser
7. D. Mattingly
8. C. Barceló

Citations in the corpus

• Quantum-Spacetime Phenomenology (2008, methodology): “[58, 55, 349, 140, 386, 387, 354, 388, 352, 353, 350, 26, 200, 493, 465, 291, 314, 366] and references therein), but for the purposes of this review I shall limit my consideration of DSR ideas on phenomenology to a single one of the (many) relevant issues, which is an observation that concerns the c”
• Introduction to doubly special relativity (2004, background): “Next it was realized in [18], [20] that the algebra of positions and Lorentz charges is nothing but de Sitter SO(4, 1) algebra.”
• Doubly special relativity and de Sitter space (2003, unknown): “It has been shown in the recent paper [21] that all these properties can be understood if one employs a simple geometrical language.”
• 2+1 gravity and doubly special relativity (2003, background): “This (quantum) algebraic construction has a geometrical counterpart, described in [29], [30].”
• Analogue Gravity (2005, background): “• Numerous suggestions regarding a minimum length in quantum gravity [32, 35, 49, 85, 135, 175, 176, 215, 216, 217, 243, 245, 244, 355].”
• Principle of relative locality (2011, background): “Last but not least, momentum spaces of constant curvature find its natural application as a model of Doubly (or deformed) Special Relativity (DSR) [28–30, 32], whose second observer independent scale is naturally associated with the curvature of the momentum space [30]10 (see also [31].”