Markovian representations of current algebras

Abstract

Hegerfeldt's (1974) concept of T-positivity in Euclidean random fields is generalised to non-commutative probability theory, that is, to Euclidean Fermi fields and to current algebra with possible Schwinger terms. The axioms imply the Wightman axioms. A non-Abelian form of Markovicity is introduced, and is shown to imply T-positivity if a reflection property holds. The investigation suggests a generalization of Nelson-Symanzik positivity, which might be valid in cases when the extension of the Schwinger functions to coinciding arguments is not expected to maintain both commutativity and positivity (or anti-commutativity and positivity).