|
| | | | |
| | | |
| Stat |
Members: 3645
Articles: 2'504'928
Articles rated: 2609
25 April 2024 |
|
| | | | |
|
Article overview
| |
|
|
Cluster Convergence Theorem | | Chris Austin
; | | Date: |
4 Sep 2005 | | Subject: | hep-th | | Abstract: | A power-counting theorem is presented, that is designed to play an analogous role, in the proof of a BPHZ convergence theorem, in Euclidean position space, to the role played by Weinberg’s power-counting theorem, in Zimmermann’s proof of the BPHZ convergence theorem, in momentum space. If $x$ denotes a position space configuration, of the vertices, of a Feynman diagram, and $sigma$ is a real number, such that $0 < sigma < 1$, a $sigma$-cluster, of $x$, is a nonempty subset, $J$, of the vertices of the diagram, such that the maximum distance, between any two vertices, in $J$, is less than $sigma$, times the minimum distance, from any vertex, in $J$, to any vertex, not in $J$. The set of all the $sigma$-clusters, of $x$, has similar combinatoric properties to a forest, and the configuration space, of the vertices, is cut up into a finite number of sectors, classified by the set of all their $sigma$-clusters. It is proved that if, for each such sector, the integrand can be bounded by an expression, that satisfies a certain power-counting requirement, for each $sigma$-cluster, then the integral, over the position, of any one vertex, is absolutely convergent, and the result can be bounded by the sum of a finite number of expressions, of the same type, each of which satisfies the corresponding power-counting requirements. | | Source: | arXiv, hep-th/0509033 | | Services: | Forum | Review | PDF | Favorites | |
|
|
No review found.
Did you like this article?
Note: answers to reviews or questions about the article must be posted in the forum section.
Authors are not allowed to review their own article. They can use the forum section.
browser Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)
|
| |
|
|
|
|
News, job offers and information for researchers and scientists:
| |
REGISTER