On Some New Proof of the Bogoliubov-Parasiuk Theorem (Nonequilibrium Renormalization Theory II)

TL;DR

This paper introduces a simplified combinatorial proof of the Bogoliubov-Parasiuk theorem by interpreting Feynman amplitudes as distributions on alpha-parameter space, facilitating future work on nonequilibrium divergence subtraction.

Contribution

It provides a new, simpler combinatorial proof of the Bogoliubov-Parasiuk theorem using distributional interpretation of Feynman amplitudes.

Findings

Simplified proof of the Bogoliubov-Parasiuk theorem

Interpretation of Feynman amplitudes as distributions on alpha-parameters

Framework for future divergence subtraction in nonequilibrium diagrams

Abstract

It is usually used a complicated combinatorics to prove the Bogoliubov-Parasiuk theorem. In the present paper we give a proof of the Bogoliubov-Parasiuk theorem which use a simple combinatorics. To give this proof we interpret Feynman amplitudes as distributions on the space of \alpha-parameters. We will use this technique in the next paper to give a proof that the divergences in nonequilibrium diagram technique can be subtracted by means the counterterms of asymptotical state.