Topological quantum field theory

Topological quantum field theory in theoretical physics provides an example of background-independent quantum theory, but with no local degrees of freedom, and only finitely many degrees of freedom globally. This is inadequate to describe gravity in four dimensions, which even in vacuum has local degrees of freedom according to general relativity.

Related Topics:
Theoretical physics - Quantum theory - Degrees of freedom - Gravity - Vacuum - General relativity

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See also Chern-Simons, BF model

Related Topics:
Chern-Simons - BF model

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There is a formulation of an n-dimensional topological quantum field theory using cobordisms and category theory. Take the category of n-1 dimensional compact boundaryless manifolds with smooth maps. Cobordisms form a category with the n-1 dimensional compact boundariless manifolds as objects. There is a functor to the category of complex vector spaces. Both the cobordism category and the category of complex vector spaces are monoidal categories. The functor respects that.

Related Topics:
Cobordism - Category theory - Functor

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