Structure, Classification, and Conformal Symmetry, of Elementary Particles over Non-Archimedean Space–Time

Conformal Geometry and Elementary Particles.

Global Newton Iteration over Archimedean and non-Archimedean Fields

In this paper, we study iterative methods on the coefficients of the rational univariate representation (RUR) of a given algebraic set, called global Newton iteration. We compare two natural approaches to define locally quadratically convergent iterations: the first one involves Newton iteration applied to the approximate roots individually and then interpolation to find the RUR of these approx...

Gauged Duality, Conformal Symmetry and Spacetime with Two Timesa

We construct a duality between several simple physical systems by showing that they are different aspects of the same quantum theory. Examples include the free relativistic massless particle and the hydrogen atom in any number of dimensions. The key is the gauging of the Sp(2) duality symmetry that treats position and momentum (x, p) as a doublet in phase space. As a consequence of the gauging,...

Conformal p-branes as a source of structure in spacetime.

On the Classification of Rank 1 Groups over Non-archimedean Local Fields

We outline the classification of K-rank 1 groups over non-archimedean local fields K up to strict isogeny, as in [Ti1] and [Ti2]. We outline the classification of absolutely simple algebraic groups over non-archimedean local fields, up to strict isogeny. This is classical, and accounts of it have been written by Tits ([Ti1], [Ti2]) and Satake ([Sa]). Tits compiled tables of ‘admissible indices’...