On some Markov processes arising from the Eyre-Hudson super Lie algebra representations

It is well-known(3,5) that Brownian motion and Poisson process arise natura lly from the canonical commutation relations (CCR) of free field operators in a boson Fock space. Eyre and Hudson(2) have recently shown how to constr uct fields of operators in a boson Fock space obeying super Lie commutation relations. We establish the essential self-adjointness of their real and i maginary parts on the domain E, the linear manifold generated by all the ex ponential (coherent) vectors and determine a family of Markov processes whi ch they give rise to in a natural manner. These Markov processes yield exam ples of Evans-Hudson flows(3,5) and Azema-like martingales.(1,4,6)