Infinitely divisible representations of Clifford algebras

by D. Mathon and R. F. Streater; Zeits. fur Wahrschein. Werw. Geb., 20, 308-316, 1971.

ABSTRACT

We define the notion of infinitely divisible representation for a Clifford algebra. We show that a representation is infinitely divisible (relative to a cyclic vector) if and only if the corresponding state is quasi-free.

REMARKS

Much later, an alternative proof, which also applies to the CAR-algebra, was found: click here.

This work, and that in Lie algebras, was later unified and generalised by Michael Schurmann. A new idea, that of free probability, was invented by Voiculescu. Some of the flavour of this subject can be seen here