Geodesic
Generalized Functions for Quantum Fields Obeying Quadratic Exchange Relations
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Problems of the modern mathematical physics, Tome 228 (2000), pp. 90-100

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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. 
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     author = {H. Grosse and M. Oberguggenberger and I. T. Todorov},
     title = {Generalized {Functions} for {Quantum} {Fields} {Obeying} {Quadratic} {Exchange} {Relations}},
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     pages = {90--100},
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     year = {2000},
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     url = {http://geodesic.mathdoc.fr/item/TM_2000_228_a7/}
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H. Grosse; M. Oberguggenberger; I. T. Todorov. Generalized Functions for Quantum Fields Obeying Quadratic Exchange Relations. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Problems of the modern mathematical physics, Tome 228 (2000), pp. 90-100. http://geodesic.mathdoc.fr/item/TM_2000_228_a7/