Year: 2008
Type: article
Abstract: The formulation of a quantum theory of gravitation has been a goal for theoretical physicists since the birth of quantum mechanics. Applying quantum mechanics to high energy processes in the framework of general relativity leads to the operational noncommutativity of spacetime coordinates. Noncommutative spacetime geometries are also obtained in open string theories at certain low energy limits. A theory of gravitation on noncommutative spacetime could be compatible with quantum mechanics and be able to capture the expected nonlocality of physics at very small distances and high energies, and also be able to reproduce Einstein's general relativity at long distances. In this work I investigate gravitation as a gauge theory of the Poincaré symmetry and I aim at generalizing this point of view to noncommutative spacetimes. First I review the important role of the Poincaré symmetry in relativistic physics and the derivation of the classical theory of gravitation as a gauge theory of the Poincaré symmetry. I continue by discussing noncommutative spaces and the formulation of quantum field theories on noncommutative spacetimes. The formulation of noncommutative gauge theories is explained carefully due to the local nature of gauge symmetries. Special emphasis is given to the twisted Poincaré symmetry, a new quantum symmetry of noncommutative spacetime, that is respected by these theories. Challenges encountered in the formulation of noncommutative gravitation and their solutions suggested in literature are discussed. I explain how all the approaches made so far lack the fundamental property of covariance under the general coordinate transformations, the cornerstone of general relativity. Finally, I study the possibility to generalize the twisted Poincaré symmetry to a local gauge symmetry in noncommutative spacetime — in the hope to obtain a noncommutative gauge theory of gravitation. I show that such a generalization cannot be achieved by deforming the Poincaré symmetry by a covariant twist element. Thus other approaches to noncommutative gravitation and the twisted Poincaré symmetry will have to be considered in the future.
Source: Työväentutkimus Vuosikirja
Author: Markku Oksanen
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1159118552