Examples of Noncommutative Spaces
- In Weyl quantization, the symplectic phase space of classical mechanics is deformed into a non-commutative phase space generated by the position and momentum operators.
- The standard model of particle physics is another example of a noncommutative geometry, cf noncommutative standard model.
- The noncommutative torus, deformation of the function algebra of the ordinary torus, can be given the structure of a spectral triple. This class of examples has been studied intensively and still functions as a test case for more complicated situations.
- Snyder space
- Noncommutative algebras arising from foliations.
- Examples related to dynamical systems arising from number theory, such as the Gauss shift on continued fractions, give rise to noncommutative algebras that appear to have interesting noncommutative geometries.
Read more about this topic: Noncommutative Geometry
Famous quotes containing the words examples of, examples and/or spaces:
“Histories are more full of examples of the fidelity of dogs than of friends.”
—Alexander Pope (1688–1744)
“It is hardly to be believed how spiritual reflections when mixed with a little physics can hold people’s attention and give them a livelier idea of God than do the often ill-applied examples of his wrath.”
—G.C. (Georg Christoph)
“In any case, raw aggression is thought to be the peculiar province of men, as nurturing is the peculiar province of women.... The psychologist Erik Erikson discovered that, while little girls playing with blocks generally create pleasant interior spaces and attractive entrances, little boys are inclined to pile up the blocks as high as they can and then watch them fall down: “the contemplation of ruins,” Erikson observes, “is a masculine specialty.””
—Joyce Carol Oates (b. 1938)