A probability space is a pair () where is an algebra and ϕ is a state on the algebra. In classical probability, is the algebra of linear combinations of indicator functions on the sample space, and in quantum probability, is the Heisenberg or Clifford algebra. However, other algebras are of interest in noncommutative probability. After a short review of the framework of classical and quantum probability, other noncommutative probability spaces are discussed, in particular those associated with noncommutative space-time.
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2019
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