# Jerusalem Mathematics Colloquium

á"ñùú ,åìñëá ç'ë ,éùéîç
íåé

äëåðç
ìù
éùéîç
øð

Thursday, 13th December 2001, 4:00 pm

Mathematics Building, Lecture Hall 2

##

Prof. Yaakov Friedman

(Jerusalem College of Technology)

A New Model for Physics based on Mathematics of Symmetric Domains

** Abstract: **

Bounded Symmetric Domains are domains with a rich group
of automorphisms. There is a ternary product structure
uniquely associated with the domain.

The ball of all possible velocities is a Bounded Symmetric
Domain with respect to the Lorenz group. The generators
of this group can be identified with relativistic fields,
for instance with the electromagnetic field. Under this
representation the formulae for non-commutation of rotations
and boosts is complicated. However, replacing the velocity
by the so-called symmetric velocity, that is its relativistic
half, simplifies the above non-commutation formulae.
Conformal maps on these velocities represent the Lorentz group.
The generators of this presentation lead to the spin triple
product, which is related to the Geometric product (also
called the Clifford product). The latter simplifies greatly
the Maxwell equation, the Dirac equaion and other equations
of physics.

The measuring process defines the geometry of the state space
of a Quantum system. This geometry leads to a ternary product,
converting the state space into a Bounded Symmetric Domain.

Coffee, Cookies at the faculty lounge at 3:30.

List of talks, 2001-02

List of talks, 2000-01

List of talks, 1998-99

List of talks, 1997-98