Recently I have started reading some materials on non-commutative probability. IN this area mathematicians sometimes consider quantum theory as a non-commutative version of classical probability, with some extra conditions. With this starting point axiomatic version of quantum field theory has also been tried to construct. Based on tensor product types, bosonic and fermionic systems come up naturally. I want to know about the third type of noncommutative probability, i.e. free probability. This has been introduced by Voiculescu to attack the free group factor isomorphism problems. Is there any physical significance of free probability? Does there exists any connections between free probability and some physical systems (like symmetric and antisymmetric tensor product had with bosonic and fermionic systems).
Advanced thanks for any reply. Also please provide some references (paper or books), which describes such connection(s), if exists,