1999/02/05 by H. Grosse, Grosse, H., M. Oberguggenberger +3
Mathematics · Physics and Astronomy · #46F10 #46F20 #81T10 #81T40 #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.MP #msc:46F10 #msc:46F20 #msc:81T10 #msc:81T40
paper · pdf · doi:10.48550/arxiv.math-ph/9902008
15 pages, LATEX
arxiv created 1999/02/05 · arxiv updated 2009/11/30
The axiomatic formulation of quantum field theory (QFT) of the 1950's in terms of fields defined as operator valued Schwartz distributions is re-examined in the light of subsequent developments. These include, on the physical side, the construction of a wealth of (2-dimensional) soluble QFT models with quadratic exchange relations, and, on the mathematical side, the introduction of the Colombeau algebras of generalized functions. Exploiting the fact that energy positivity gives rise to a natural regularization of Wightman distributions as analytic functions in a tube domain, we argue that the flexible notions of Colombeau theory which can exploit particular regularizations is better suited (than Schwartz distributions) for a mathematical formulation of QFT.