Noncommutative quantum field theory

In mathematical physics, noncommutative quantum field theory (or quantum field theory on noncommutative spacetime) is an application of noncommutative mathematics to the spacetime of quantum field theory that is an outgrowth of noncommutative geometry and index theory in which the coordinate functions are noncommutative. One commonly studied version of such theories has the "canonical" commutation relation: [ x μ , x ν ] = i θ μ ν {\displaystyle [x^{\mu },x^{\nu }]=i\theta ^{\mu \nu }\,\! } where x μ {\displaystyle x^{\mu }} and x ν {\displaystyle x^{\nu }} are the hermitian generators of a noncommutative C ∗ {\displaystyle C^{*}} -algebra of "functions on spacetime".

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