A probability space is a pair ($\mathcal{ A},\phi $) where $\mathcal{ A}$ is an algebra and $\phi $ a state on the algebra. In classical probability $\mathcal{ A}$ is the algebra of linear combinations of indicator functions on the sample space and in quantum probability $\mathcal{ A}$ is the Heisenberg or Clifford algebra. However, other algebras are of interest in non-commutative probability. Here one discusses some other non-commutative probability spaces, in particular those associated to non-commutative space-time.
Categories: math.PR math-ph math.MP