Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1995-06-15
Physics
High Energy Physics
High Energy Physics - Theory
46 pages,latex, 6 .eps files representing p-adic fractals are supplied by request
Scientific paper
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.
No associations
LandOfFree
p-Adic TGD: Mathematical Ideas does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with p-Adic TGD: Mathematical Ideas, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and p-Adic TGD: Mathematical Ideas will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-590947