  In [Yu.M. Berezansky, E. Lytvynov, D. A. Mierzejewski, Ukrainian Math. J. 55
(2003), 853--858 ], the Jacobi field of a L\'evy process was derived. This
field consists of commuting self-adjoint operators acting in an extended
(interacting) Fock space. However, these operators have a quite complicated
structure. In this note, using ideas from [L. Accardi. U. Franz, M. Skeide,
Comm. Math. Phys. 228 (2002), 123--150] and [E. Lytvynov, Infin. Dimen. Anal.
Quant. Prob. Rel. Top. 7 (2004), 619--629], we obtain a unitary equivalent
representation of the Jacobi field of a L\'evy process. In this representation,
the operators act in a usual symmetric Fock space and have a much simpler
structure.
