The axiomatic formulation of quantum eld theory (QFT) of the 1950's in terms of elds deened as operator valued Schwartz distributions is reexamined 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 alge...

The axiomatic formulation of quantum eld theory (QFT) of the 1950's in terms of elds deened as operator valued Schwartz distributions is reexamined 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 alge...

In this paper, weakly homogeneous generalized functions in the special Colombeau algebras are determined up to equality in the sense of generalized distributions. This yields characterizations that are formally similar to distribution theory. Further, we give several characterizations of equality in the sense of generalized distributions in these algebras.

A straightforward introduction to the theory of Colombeau generalized functions is given with an emphasis on the underlying concepts in view of their applications to applied and theoretical problems by physicists who do not need to know all the mathematical intricacies of that theory. As an application the meaning of the square of the delta function is discussed in some detail.

We study generalized group actions on differentiable manifolds in the Colombeau framework, extending previous work on flows of generalized vector fields and symmetry group analysis of generalized solutions. As an application, we analyze group invariant generalized functions in this setting. Mathematics Subject Classification (2000): Primary: 46F30; secondary: 46T30, 35A30, 58E40

We introduce a Stieltjes transform on the equivalence classes of a new generalized function which has been successfully developed by Colombeau. Subsets of rapid descent test functions, (Rn), as well as tempered distributions, ′(Rn), are used to preserve Fourier analysis techniques. 2000 Mathematics Subject Classification. Primary 46F12.