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.
CITATION STYLE
Kerner, R. (2007). Non-commutative Extensions of Classical Theories in Physics. In Towards Quantum Gravity (pp. 130–157). Springer Berlin Heidelberg. https://doi.org/10.1007/3-540-46634-7_6
Mendeley helps you to discover research relevant for your work.