Non-commutative space-time of Doubly Special Relativity theories

By Jerzy Kowalski-Glikman, S. Nowak. 2002

209 citations recorded by the source corpus.

Doubly Special Relativity (DSR) theory is a recently proposed theory with two observer-independent scales (of velocity and mass), which is to describe a kinematic structure underlining the theory of Quantum Gravity. We observe that there are infinitely many DSR constructions of the energy–momentum sector, each of whose can be promoted to the κ-Poincare quantum (Hopf) algebra. Then we use the co-product of this algebra and the Heisenberg double construction of κ-deformed phase space in order to derive the non-commutative space–time structure and the description of the whole of DSR phase space. Next we show that contrary to the ambiguous structure of the energy momentum sector, the space–time of the DSR theory is unique and related to the theory with non-commutative space–time proposed long ago by Snyder. This theory provides non-commutative version of Minkowski space–time enjoying ordinary Lorentz symmetry. It turns out that when one builds a natural phase space on this space–time, its intrinsic length par...

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/36a076d02f4b1e1f0ec63bd66f72761039c50b79

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Citations in the corpus

Modern Tests of Lorentz Invariance (2005, background): “For discussions of other types of non-commutativity, including those that preserve Lorentz invariance or lead to DSR-type theories see [187, 225].”
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”
2+1 gravity and doubly special relativity (2003, methodology): “Taking the co-algebra of the κ-Poincaré quantum algebra and using the so-called “Heisenberg-double construction” [26], [27], [28] it is possible to derive the position variables, conjugate to momenta, xμ, as well as the brackets between them and the κ-Poincaré algebra generators.”
Ponzano–Regge model revisited: III. Feynman diagrams and effective field theory (2005, background): “This is nicely exemplified in [5] for the 3 + 1 κ-Poincaré algebra and in [12] for the 2 + 1 κ-Poincaré algebra.”
Doubly special relativity and de Sitter space (2003, unknown): “One should note at this point that, as proved in [17] the commutators (45) are basis independent, because in the Heisenberg double procedure they picked up contributions from the first order terms in co-product, that are left unchanged if one turns from one DSR basis to another.”
Planck-scale modified dispersion relations and Finsler geometry (2006, unknown): “[21, 26]).”
Deformed special relativity as an effective flat limit of quantum gravity (2004, background): “The geometrical picture is a non-commutative space-time with a curved momentum space (either de Sitter or Anti de Sitter) [1, 4].”