Proof of the Bogoliubov-Parasiuk theorem on renormalization. (English) Zbl 1222.81219

Hepp, Klaus

Commun. Math. Phys. 2, No. 4, 301-326 (1966).

Summary: A new proof is given that the subtraction rules of Bogoliubov and Parasiuk lead to well-defined renormalized Green’s distributions. A collection of the counter-terms in “trees” removes the difficulties with overlapping divergences and allows fairly simple estimates and closed expressions for renormalized Feynman integrals. The renormalization procedure, which also applies to conventionally non-renormalizable theories, is illustrated in the \(\varphi^{4}\)-theory.

MSC:

81T15	Perturbative methods of renormalization applied to problems in quantum field theory
81T16	Nonperturbative methods of renormalization applied to problems in quantum field theory

References:

[1]	Bogoliubov, N. N., andO. S. Parasiuk: Acta Math.97, 227 (1957). · Zbl 0081.43302
[2]	Parasiuk, O. S.: Ukrainskii Math. J.12, 287 (1960).
[3]	Schwartz, L.: Théorie des distributions, I, II. Paris: Hermann 1957/59. · Zbl 0089.09601
[4]	Wick, G. C.: Phys. Rev.80, 268 (1950). · Zbl 0040.13006
[5]	Pauli, W., andF. Villars: Rev. Mod. Phys.21, 434 (1949). · Zbl 0037.12503
[6]	Parasiuk, O. S.: Izv. Akad. Nauk, Ser. Mat.20, 843 (1956).
[7]	Dyson, F. J.: Phys. Rev.75, 486 and 1736 (1949). · Zbl 0032.23702
[8]	Salam, A.: Phys. Rev.82, 217;84, 426 (1951). · Zbl 0042.45501
[9]	Wu, T. T.: Phys. Rev.125, 1436 (1962). · Zbl 0100.41201
[10]	Bogoliubov, N. N., andD. V. Shirkov: Introduction to the theory of quantized fields. New York: Interscience 1959. · Zbl 0088.21701