Weak mixing angles as dynamical degrees of freedom

Apsidal Angles for Symmetrical Dynamical Systems with Two Degrees of Freedom

The bob of a spherical pendulum (or particle on a smooth sphere under gravity) oscillates between two levels, and the change of azimuth in passing from the lower to the higher level, or vice versa, is the same for all such passages during a single motion. Using the language of orbit theory, we shall refer to this change of azimuth as the apsidal angle. It is a function of the two constants of t...

Dynamical Systems with Two Degrees of Freedom.

The Dynamical Degrees of Freedom in Spatially Homogeneous Cosmology*

The true analogues of superspace and conformal superspace for spatially homogeneous cosmology are introduced and discussed in relation to the kinematics of the evolution of Cauchy data from a spatially homogeneous initial value surface using a spatially homogeneous lapse function. Having fixed the slicing of spatially homogeneous spacetimes to be the natural one, an obvious restriction on the f...

Variational Integrators for Dynamical Systems with Rotational Degrees of Freedom

For the elastodynamic simulation of a geometrically exact beam, a variational integrator is derived from a PDE viewpoint. Variational integrators are symplectic and conserve discrete momentum maps and since the presented integrator is derived in the Lie group setting (unit quaternions for the representation of rotational degrees of freedom), it intrinsically preserves the group structure withou...

Matrix Elements and the Determination of the Weak Mixing Angles

The main goal of this talk is to review a new method’ for predicting, from QCD, the weak matrix elements that are needed to describe the semileptonic decays; B -+ DePe,,B + D’ec, and Ab + A,eti,. The method also relates B + pe& semileptonic decay to D + pZuc semileptonic decay. Since these are exclusive decays involving hadronic states nonperturbative strong interaction physics plays a role. Th...