New dynamical degrees of freedom from invertible transformations

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...

Invertible Darboux Transformations

For operators of many different kinds it has been proved that (generalized) Darboux transformations can be built using so called Wronskian formulae. Such Darboux transformations are not invertible in the sense that the corresponding mappings of the operator kernels are not invertible. The only known invertible ones were Laplace transformations (and their compositions), which are special cases o...

Hadronic Degrees of Freedom

The point of view I take to summarize some of the research activities in Italy in the field of hadronic physics, is determined by the (today accepted) fundamental degrees of freedom of the strong interactions, namely quarks and gluons. The Sec. 2 is devoted to the link of the fundamental theory of strong interactions, Quantum Chromodynamics (QCD), with effective degrees of freedom often used to...