Non-commutative extensions of classical theories in physics

Details Non-commutative extensions of classical theories in physics Non-commutative extensions of classical theories in physics

2000-04-26

arxiv.org/abs/math-ph/0004033v1

Lect.Notes Phys. 541 (2000) 130-157

Physics

Mathematical Physics

28 pages, no figures, Contribution to Proceedings of XXXV-th Karpacz Winter School of Theoretical Physics, Polanica, February

Scientific paper

We present a short introductory overview of the non-commutative extensions of several classical physical theories. After a general discussion of the reasons that suggest that the non-commutativity is a major issue that will eventually lead to the unification of gravity with other fundamental interactions, we display examples of non-commutative generalizations of known geometries. Finally we discuss the general properties of the algebras that could become generalizations of algebras of smooth functions on Minkowskian (Riemannian) manifolds, needed for the description of Quantum Gravity.

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