Integral Representations for Schwinger Functionals and the Moment Problem Over Nuclear Spaces
Jan, 197527 pages
Published in:
- Commun.Math.Phys. 43 (1975) 255
DOI:
Report number:
- Print-75-0097 (GOTTINGEN)
Citations per year
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
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