Non-commutative probability and non-commutative processes: Beyond the Heisenberg algebra

A probability space is a pair (A,phi) where A is an algebra and phi is a state on the algebra. In classical probability, A is the algebra of linear combinations of indicator functions on the sample space, and in quantum probability, A 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. Published under license by AIP Publishing.