In this research we described the effective Hamiltonian theory and applied this theory to the calculation of current-current (Q1,2) and QCD penguin (Q3,…,6) c quark decay rates. We calculated the decay rates of semileptonic and hadronic of charm quark in the effective Hamiltonian theory. We investigated the decay rates of D meson decays according to Spectator Quark Model (SQM) for the calculati...

A generalization of the method of Chu, Liu and Mehrmann [7] for the computation of the Hamiltonian real Schur form is presented. The new method avoids some of the difficulties that may arise when a Hamiltonian matrix has tightly clustered groups of eigenvalues. A detailed analysis of the method is presented and several numerical examples demonstrate the superior behavior of the method.

In this thesis, we consider smooth optimal control systems that evolve on Lie groups. Pontryagin’s maximum principle allows us to search for local solutions of the optimal control problem by studying an associated Hamiltonian dynamical system. When the associated Hamiltonian function possess symmetries, we can often study the Hamiltonian system in a vector space whose dimension is lower than th...

Aspects of noncanonical Hamiltonian field theory are reviewed. '·1any systems are Hamiltonian in the sense of possessing Poisson bracket structures, yet the equations are not in canonical form. A particular sys tem of thi s type is cons idered, namely reduced magnetohydrodynamics (RllHD) which was derived for tokamak modelling. The notion of a liePoisson bracket is reviewed; these are special P...

Aspects of noncanonical Hamiltonian field theory are reviewed. f·1any systems are Hamiltonian in the sense of possessing Poisson bracket structures. yet the equations are not in canonical form. A particular system of this type is considered. namely reduced magnetohydrodynamics (RflHD) which was derived for tokamak modelling. The notion of a LiePoisson bracket is reviewed; these are special Pois...

Aspects of noncanonical Hamiltonian field theory are reviewed. '·1any systems are Hamiltonian in the sense of possessing Poisson bracket structures, yet the equations are not in canonical form. A particular sys tem of thi s type is cons idered, namely reduced magnetohydrodynamics (RllHD) which was derived for tokamak modelling. The notion of a liePoisson bracket is reviewed; these are special P...

It is well known that the integrable Hamiltonian systems defined by the Adler-Kostant-Symes construction correspond via Hamiltonian reduction to systems on cotangent bundles of Lie groups. Generalizing previous results on Toda systems, here a Lagrangian version of the reduction procedure is exhibited for those cases for which the underlying Lie algebra admits an invariant scalar product. This i...

Hamiltonian LGT in the complete Fourier analysis basis. The main problem in the Hamiltonian formulation of Lattice Gauge Theories is the determination of an appropriate basis avoiding the over-completeness arising from Mandelstam relations. We shortcut this problem using Harmonic analysis on Lie-Groups and intertwining operators formalism to explicitly construct a basis of the Hilbert space. Ou...

The Lie group adiabatic evolution determined by a Lie algebra parameter dependent Hamiltonian is considered. It is demonstrated that in the case when the parameter space of the Hamiltonian is a homogeneous Kähler manifold its fundamental Kähler potentials completely determine Berry geometrical phase factor. Explicit expressions for Berry vector potentials (Berry connections) and Berry curvature...