Physics
Seminars

Monday, July 18, 2005

10:30 am & 2:30 pm

Willet Science Center 101

10:30 am
and
We seek all linear transformations
of the Maxwell variables and spacetime coordinates that leave Maxwell's
equations form-invariant. Form-invariance forces coordinate transformations
to leave the Minkowski interval invariant allowing five different four-dimensional
Lorentz spacetimes, one real and four complex, corresponding to coordinate
transformations under the (1/2,1/2), (0,0)+(0,1), (0,0)+(1,0),
(1/2,0)+(1/2,0), and (0,1/2)+(0,1/2) representations of the Lorentz group. In
each spacetime, Maxwell's equations remain covariant under at least |

2:30 pm
& ApplSci Inc. A quantum geometrodynamical
approach is developed for the computation of unified mass-spacetimes (MST).
The resulting theory of the evolution of quantum dynamical manifolds (QDMs)
is shown to contain contemporary quantum mechanics. This approach overcomes a
major obstacle in Yang-Mills theories that generalize Maxwell’s equations.
The process used transforms the basis of abstract vectors defining the geometry
of the QDM so that the equations of the geometrodynamical extension of quantum
mechanics, called quantum dynamical manifold equations (QDMEs), can be put into
a canonical form. This places the effects causing problems in Yang-Mills theories
into the abstract vector space basis in a way that the resulting equations are
integrable. The QDMEs are shown to be completely classifiable according to the
Cartan-Killing theorem of Lie algebra theory. This leads to a hierarchy of equations
that include, at lower energies, ones for manifolds with |

*Please join us for light refreshments at
10:15am and 2:15pm outside WSC 109.*