Finite-particle approximations of a local field and the problem of local saturation

B. L. Voronov, I. F. Skirko


Abstract: A study is made of the problem of approximating a nontrivial field by finite polynomials in the free fields. This problem, like the well-known problem of the local saturation of the matrix elements of the commutator of fields, reduces to the solution of a finite system of equations for the $r$-functions (nondiagonal matrix elements of the Heisenberg current). This corresponds to a definite truncation (with respect to the particle number) of the well-known infinite system of axiomatic equations for the $r$-functions of local quantum field theory.

Received: 14.04.1975

 English version: Theoretical and Mathematical Physics, 1976, 26:2, 115–124