Quantum symmetry, the cosmological constant and Planck scale phenomenology

By Giovanni Amelino-Camelia, Lee Smolin, A. Starodubtsev. 2003

225 citations recorded by the source corpus.

We present a simple algebraic mechanism for the emergence of deformations of Poincar? symmetries in the low-energy limit of quantum theories of gravity. The deformations, called ?-Poincar? algebras, are parametrized by a dimensional parameter proportional to the Planck mass, and imply modified energy?momentum relations of a type that may be observable in near future experiments. Our analysis assumes that the low energy limit of a quantum theory of gravity must also involve a limit in which the cosmological constant is taken very small with respect to the Planck scale, and makes use of the fact that in some quantum theories of gravity the cosmological constant results in the (anti)de Sitter symmetry algebra being quantum deformed. We show that deformed Poincar? symmetries inevitably emerge in the small-cosmological-constant limit of quantum gravity in 2 + 1 dimensions, where geometry does not have local degrees of freedom. In 3 + 1 dimensions we observe that, besides the quantum deformation of the (anti)de Sitter symmetry algebra, one must also take into account that there are local degrees of freedom leading to a renormalization of the generators for energy and momentum of the excitations. At the present level of development of quantum gravity in 3 + 1 dimensions, it is not yet possible to derive this renormalization from first principles, but we establish the conditions needed for the emergence of a deformed low energy limit symmetry algebra also in the case of 3 + 1 dimensions.

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

View Paper: https://www.semanticscholar.org/paper/13b4d68a35f9b933c3e1160817c898b2f816d581

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Citations in the corpus

Quantum-Spacetime Phenomenology (2008, methodology): “An example of this type is provided by Loop Quantum Gravity (LQG) [476, 96, 502, 524, 93], where one is presently unable to even formulate many desirable physics questions, but at least some (however tentative) progress has been made [247, 33, 523, 75, 128] in the exploration of the kinematics of th”
Minimal Length Scale Scenarios for Quantum Gravity (2012, background): “However, there are non-rigorous arguments that DSR may emerge from a semiclassical limit of quantum gravity theories in the form of an effective field theory with an energy dependent metric [29], or that DSR (in form of a κ-Poincaré algebra) may result from a version of path integral quantization [1”