## How to Define Generalized Feynman Diagrams?

**Authors:** Matti Pitkänen

Generalized Feynman diagrams have become the central notion of quantum TGD and one
might even say that space-time surfaces can be identified as generalized Feynman diagrams. The
challenge is to assign a precise mathematical content for this notion, show their mathematical
existence, and develop a machinery for calculating them. Zero energy ontology has led to a
dramatic progress in the understanding of generalized Feynman diagrams at the level of fermionic
degrees of freedom. In particular, manifest finiteness in these degrees of freedom follows trivially
from the basic identifications as does also unitarity and non-trivial coupling constant evolution.
There are however several formidable looking challenges left.

- One should perform the functional integral over WCW degrees of freedom for fixed values of
on mass shell momenta appearing in the internal lines. After this one must perform integral
or summation over loop momenta.
- One must define the functional integral also in the p-adic context. p-Adic Fourier analysis
relying on algebraic continuation raises hopes in this respect. p-Adicity suggests strongly
that the loop momenta are discretized and ZEO predicts this kind of discretization naturally.

In this article a proposal giving excellent hopes for achieving these challenges is discussed.

**Comments:** 16 Pages.

**Download:** **PDF**

### Submission history

[v1] 16 Jun 2010

[v2] 2012-01-30 21:53:06

**Unique-IP document downloads:** 469 times

Vixra.org is a pre-print repository rather than a journal. Articles hosted may not yet have been verified by peer-review and should be treated as preliminary.
In particular, anything that appears to include financial or legal advice or proposed medical treatments should be treated with due caution.
Vixra.org will not be responsible for any consequences of actions that result from any form of use of any documents on this website.

**Add your own feedback and questions here:**

*You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful.*

*
*