Quantum Topology / Hopf Algebra Seminar
Mark Hopkins
UW-Milwaukee
Unification of Galilei, Poincare and Euclidean Symmetry
Abstract: The passage of 100 years has not uncovered all that can be said about
Relativistic Physics and its relation to Newtonian Physics and Galilean
Relativity.
Defining the Poincaré Group -> Galilei Group correspondence limit is not a
trivial exercise. Since the Galilei group has a central charge (mass),
then it is necessary to include an 11th generator into the Poincaré group
and a 5th coordinate to the underlying geometry. The result
is a unification of Galilei and Poincaré into a continuous 1-parameter
family of gauge groups that also happens to include, for free, the
4-dimensional Euclidean group and a definition of absolute time.
All members of the family are embedded in the 4+1 Poincaré group in a way
analogous to the unification of Euclidean, Hyperbolic and Spherical
geometries into projective geometry.
We will review the ramifications of the unification; revisiting such
questions, along the way, as: "What is the meaning of Euclidean
time?" and "What is the meaning of imaginary mass for tachyons?"
Tuesday October 7, 2008 at 3:00 PM in SEO 712