## 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

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