BPHZ theorem
The Bogoljubow-Parasjuk-Hepp-Zimmermann theorem , according to Nikolai Nikolajewitsch Bogoljubow , Ostap Parasjuk , Klaus Hepp and Wolfhart Zimmermann , or BPHZ theorem for short , is a proposition from the quantum field theory . It was established by Bogolyubov and Parasjuk in 1957 and largely proven. The proof was completed by Hepp in 1966. In 1969 Zimmermann published a simplified version of the proof.
The main statement of the BPHZ theorem reads: All divergences of a quantum field theory can be canceled by counterterms to superficially divergent 1-particle irreducible Feynman diagrams .
In practice this means that it is sufficient to renormalize 1-particle irreducible Feynman diagrams and that no counter terms for reducible Feynman diagrams have to be introduced.
Individual evidence
- ↑ NN Bogoliubow and OS Parasiuk: On the multiplication of the causal functions in the quantum theory of fields . In: Acta Math. Band 97 , 1957, pp. 227-266 , doi : 10.1007 / BF02392399 .
- ^ Klaus Hepp: Proof of the Bogoliubov-Parasiuk Theorem on Renormalization . In: Communications in Mathematical Physics . tape 2 , no. 1 , 1966, p. 301–326 , doi : 10.1007 / BF01773358 (English).
- ^ W. Zimmermann: Convergence of Bogoliubov's Method of Renormalization in Momentum Space . In: Communications in Mathematical Physics . tape 15 , no. 3 , 1969, p. 208-234 , doi : 10.1007 / BF01645676 (English).
- ^ Matthew D. Schwartz: Quantum Field Theory and the Standard Model . Cambridge University Press, Cambridge 2014, ISBN 978-1-107-03473-0 , pp. 385 (English).