Integral Representations for Schwinger Functionals and the Moment Problem Over Nuclear Spaces

Jan, 1975
27 pages
Published in:
  • Commun.Math.Phys. 43 (1975) 255
Report number:
  • Print-75-0097 (GOTTINGEN)

Citations per year

19751986199720082018102
Abstract: (Springer)
It is shown that a continuous positive linear functional on a commutative nuclear *-algebra has an integral decomposition into characters if and only if the functional is strongly positive, i.e. positive on all positive polynomials. When applied to the symmetric tensor algebra over a nuclear test function space this gives a necessary and sufficient condition for the Schwinger functions of Euclidean quantum field theory to be the moments of a continuous cylinder measure on the dual space. Another application is to the problem of decomposing a Wightman functional into states having the cluster property.
  • AXIOMATIC FIELD THEORY
  • FIELD THEORY: OPERATOR ALGEBRA
  • MOMENT