Axiomatic field theory in terms of operator Jacobi matrices

It is shown that the Wightman axiomatic theory of an tlermitian scalar field can be reformulated in terms of operator Jacobi matrices in analogy with the transition to Jacobi matrices in the problem of moments. This reformulation ieads naturally to the concept of a quasifield, an object that is simpler than a field. The generating funetionals that define the quasifield and are reiated to the Wightman functionals are studied. In the case of a free field, specification of the latter by creation and annihilation operators is identical with the specification in terms of Jacobi matrices.