Skip to main content
We gratefully acknowledge support from the Simons Foundation, member institutions, and all contributors. Donate
arXiv logo
Cornell University Logo

Mathematical Physics

arXiv:1804.08031 (math-ph)
[Submitted on 21 Apr 2018 (v1), last revised 30 Aug 2018 (this version, v2)]

Title:A combinatorial matrix approach for the generation of vacuum Feynman graphs multiplicities in $ϕ^4$ theory

Authors:Erick Castro, Itzhak Roditi
View PDF
Abstract:From the standard procedure for constructing Feynman vacuum graphs in $\phi^4$ theory from the generating functional $Z$, we find a relation with sets of certain combinatorial matrices, which allows us to generate the set of all Feynman graphs and the respective multiplicities in an equivalent combinatoric way. These combinatorial matrices are explicitly related with the permutation group, which facilitates the construction of the vacuum Feynman graphs. Various insights in this combinatoric problem are proposed, which in principle provide an efficient way to compute the Feynman vacuum graphs and its multiplicities.
Comments: 27 pages
Subjects: Mathematical Physics (math-ph); High Energy Physics - Theory (hep-th)
Cite as: arXiv:1804.08031 [math-ph]
  (or arXiv:1804.08031v2 [math-ph] for this version)
  https://doi.org/10.48550/arXiv.1804.08031
Journal reference: J. Phys. A: Math. Theor. 51 (2018) 395202 (34pp)
Related DOI: https://doi.org/10.1088/1751-8121/aad9b4

Submission history

From: Erick Castro [view email]
[v1] Sat, 21 Apr 2018 21:41:19 UTC (409 KB)
[v2] Thu, 30 Aug 2018 17:06:48 UTC (414 KB)
Full-text links:

Access Paper:

  • View PDF
  • TeX Source
  • Other Formats
view license
Current browse context:
math-ph
< prev   |   next >
new | recent | 2018-04
Change to browse by:
hep-th
math
math.MP

References & Citations

1 blog link

(what is this?)
export BibTeX citation

Bookmark

BibSonomy logo Reddit logo

Bibliographic and Citation Tools

Bibliographic Explorer (What is the Explorer?)
Connected Papers (What is Connected Papers?)
Litmaps (What is Litmaps?)
scite Smart Citations (What are Smart Citations?)

Code, Data and Media Associated with this Article

alphaXiv (What is alphaXiv?)
CatalyzeX Code Finder for Papers (What is CatalyzeX?)
DagsHub (What is DagsHub?)
Gotit.pub (What is GotitPub?)
Hugging Face (What is Huggingface?)
Papers with Code (What is Papers with Code?)
ScienceCast (What is ScienceCast?)

Demos

Replicate (What is Replicate?)
Hugging Face Spaces (What is Spaces?)
TXYZ.AI (What is TXYZ.AI?)

Recommenders and Search Tools

Influence Flower (What are Influence Flowers?)
CORE Recommender (What is CORE?)

arXivLabs: experimental projects with community collaborators

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.

Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)