2+1 gravity and doubly special relativity

By L. Freidel, Jerzy Kowalski-Glikman, Lee Smolin. 2003

154 citations recorded by the source corpus.

It is shown that gravity in 2+1 dimensions coupled to point particles provides a nontrivial example of doubly special relativity (DSR). This result is obtained by interpretation of previous results in the field and by exhibiting an explicit transformation between the phase space algebra for one particle in 2+1 gravity found by Matschull and Welling and the corresponding DSR algebra. The identification of 2+1 gravity as a DSR system answers a number of questions concerning the latter, and resolves the ambiguity of the basis of the algebra of observables. Based on this observation a heuristic argument is made that the algebra of symmetries of ultra high energy particle kinematics in 3+1 dimensions is described by some DSR theory.

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

View Paper: https://www.semanticscholar.org/paper/dc97771e8f3fc275a34c19ca9d58b6afd52ab89b

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Citations in the corpus

Quantum-Spacetime Phenomenology (2008, background): “[75, 237, 259, 238], specifically a spacetime with “Lie-algebra noncommutativity””
Ponzano–Regge model revisited: III. Feynman diagrams and effective field theory (2005, methodology): “This is nicely exemplified in [5] for the 3 + 1 κ-Poincaré algebra and in [12] for the 2 + 1 κ-Poincaré algebra.”
Planck-scale modified dispersion relations and Finsler geometry (2006, background): “While some promising results linking DSR to some special form of spacetime noncommutativity have been found in 2+1 dimensions [27], we are still lacking a consistent physical picture in 3+1 dimensions.”
Principle of relative locality (2011, methodology): “It is by now well established by different methods [15–22] that in 2+1 dimensions, where gravity is described by a topological field theory [23], the effective momentum space of particles is deformed and becomes a (curved) three dimensional group manifold.”
Minimal Length Scale Scenarios for Quantum Gravity (2012, background): “In addition, it has been shown that in 2+1 dimensional gravity coupled to matter, the gravitational degrees of freedom can be integrated out, leaving an effective field theory for the matter, which is a quantum field theory on κ-Minkowski spacetime, realizing a particular version of DSR [114].”
Ponzano–Regge model revisited: I. Gauge fixing, observables and interacting spinning particles (2004, background): “This property is characteristic of a theory exhibiting the symmetry of Doubly Special Relativity [43].”
Tests of Lorentz invariance: a 2013 update (2013, background): “Such momentum space constructions have been linked to possible Lie-type non-commutative geometry (mainly the so-called kappa-Minkowski one [235, 236]) or to curved momentum spaces in higher dimensions [237].”
Doubly special relativity and de Sitter space (2003, unknown): “Recently it was shown that 2+1 gravity provides an example of a DSR theory [10], [9].”