p-Adic TGD: Mathematical Ideas
| dc.creator | Pitkänen, M. | |
| dc.date | 1995-06-15 | |
| dc.date | 1995-06-16 | |
| dc.date.accessioned | 2026-07-07T09:03:59Z | |
| dc.date.available | 2026-07-07T09:03:59Z | |
| dc.description | The mathematical basis of p-adic Higgs mechanism discussed in papers hep-th@xxx.lanl.gov 9410058-62 is considered in this paper. The basic properties of p-adic numbers, of their algebraic extensions and the so called canonical identification between positive real numbers and p-adic numbers are described. Canonical identification induces p-adic topology and differentiable structure on real axis and allows definition of definite integral with physically desired properties. p-Adic numbers together with canonical identification provide analytic tool to produce fractals. Canonical identification makes it possible to generalize probability concept, Hilbert space concept, Riemannian metric and Lie groups to p-adic context. Conformal invariance generalizes to arbitrary dimensions since p-adic numbers allow algebraic extensions of arbitrary dimension. The central theme of all developments is the existence of square root, which forces unique algebraic extension with dimension $D=4$ and $D=8$ for $p>2$ and $p=2$ respectively. This in turn implies that the dimensions of p-adic Riemann spaces are multiples of $4$ in $p>2$ case and of $8$ in $p=2$ case. | |
| dc.description | 46 pages,latex, 6 .eps files representing p-adic fractals are supplied by request | |
| dc.identifier | https://arxiv.org/abs/hep-th/9506097 | |
| dc.identifier | http://arxiv.org/abs/hep-th/9506097 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/149216 | |
| dc.subject | High Energy Physics - Theory | |
| dc.title | p-Adic TGD: Mathematical Ideas | |
| dc.type | text |