Geodesic
Generalized Functions for Quantum Fields Obeying Quadratic Exchange Relations
Informatics and Automation, Problems of the modern mathematical physics, Tome 228 (2000), pp. 90-100.

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{TRSPY_2000_228_a7,
     author = {H. Grosse and M. Oberguggenberger and I. T. Todorov},
     title = {Generalized {Functions} for {Quantum} {Fields} {Obeying} {Quadratic} {Exchange} {Relations}},
     journal = {Informatics and Automation},
     pages = {90--100},
     publisher = {mathdoc},
     volume = {228},
     year = {2000},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2000_228_a7/}
}
TY  - JOUR
AU  - H. Grosse
AU  - M. Oberguggenberger
AU  - I. T. Todorov
TI  - Generalized Functions for Quantum Fields Obeying Quadratic Exchange Relations
JO  - Informatics and Automation
PY  - 2000
SP  - 90
EP  - 100
VL  - 228
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TRSPY_2000_228_a7/
LA  - en
ID  - TRSPY_2000_228_a7
ER  - 
%0 Journal Article
%A H. Grosse
%A M. Oberguggenberger
%A I. T. Todorov
%T Generalized Functions for Quantum Fields Obeying Quadratic Exchange Relations
%J Informatics and Automation
%D 2000
%P 90-100
%V 228
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TRSPY_2000_228_a7/
%G en
%F TRSPY_2000_228_a7
H. Grosse; M. Oberguggenberger; I. T. Todorov. Generalized Functions for Quantum Fields Obeying Quadratic Exchange Relations. Informatics and Automation, Problems of the modern mathematical physics, Tome 228 (2000), pp. 90-100. http://geodesic.mathdoc.fr/item/TRSPY_2000_228_a7/

[1] Bogolubov N. N., Logunov A. A., Oksak A. I., Todorov I. T., General principles of quantum field theory, Kluwer Acad. Publ., Dordrecht, 1990 | MR | Zbl

[2] Bogolubov N. N., Shirkov D. V., Introduction to the theory of quantized fields, Wiley-Intersci., N. Y., 1959

[3] Buchholz D., Mack G., Todorov I. T., “The current algebra on the circle as a germ of local field theories”, Nucl. Phys. B Proc. Suppl., 5 (1988), 20–56 | DOI | MR

[4] Collins J., Renormalization, Cambridge Univ. Press, Cambridge, 1984 | MR

[5] Colombeau J. F., New generalized functions and multiplication of distributions, North-Holland, Amsterdam, 1985 | MR | Zbl

[6] Di Francesco P., Mathieu P., Senechal D., Conformal field theory, Springer, Berlin, 1997 | MR

[7] Haag R., Local quantum physics, Springer, Berlin, 1992 | MR

[8] Ilieva N., Thirring W., The Thirring model 40 years later, Preprint UWThPh-1998-37, Vienna, 1998 | MR

[9] Oberguggenberger M., Multiplication of distributions and application to partial differential equations, Longman, Harlow, 1992 | MR | Zbl

[10] Rosinger E. E., Nonlinear partial differential equations, North-Holland Mathematics Studies, 164, North-Holland Publishing Co., Amsterdam, 1990, An algebraic view of generalized functions | MR | Zbl

[11] Schwartz L., “Sur l'impossibilité de la multiplication des distributions”, C. R. Acad. sci. Paris, 239 (1954), 847–848 | MR | Zbl

[12] Schwartz L., Théorie des distributions, Nouvelle ed., Hermann, Paris, 1966 | MR

[13] Streater R. F., Wightman A. S., PTC, spin and statistics, and all that, 2nd ed., Benjamin/Cummings, Reading, MA, 1978

[14] Thirring W., “A soluble relativistic field theory”, Ann. Phys., 3 (1958), 91–112 | DOI | MR | Zbl