An action having an acceleration term in addition to the usual velocity term is analyzed. The quantum mechanical system is directly defined for Euclidean time using the path integral. The Euclidean Hamiltonian is shown to yield the acceleration Lagrangian and the path integral with the correct boundary conditions. Due to the acceleration term, the state space depends on both position and veloci...

Via compression ([11, 7]) we write the n-dimensional Chaplygin sphere system as an almost Hamiltonian system on T SO(n) with internal symmetry group SO(n− 1). We show how this symmetry group can be factored out, and pass to the fully reduced system on (a fiber bundle over) T S. This approach yields an explicit description of the reduced system in terms of the geometric data involved. Due to thi...

We propose a Lax equation for the non-linear sigma model which leads directly to the conserved local charges of the system. We show that the system has two infinite sets of such conserved charges following from the Lax equation, much like dispersionless systems. We show that the system has two Hamiltonian structures which are compatible so that it is truly a bi-Hamiltonian system. However, the ...

In this paper we provide explicit formulas for the number of elements/subgroups/cyclic subgroups of a given order and for the total number of subgroups/cyclic subgroups in a finite Hamiltonian group. The coverings with three proper subgroups and the principal series of such a group are also counted. Finally, we give a complete description of the lattice of characteristic subgroups of a finite H...

We give a Hamiltonian analysis of the asymptotically flat spherically symmetric system of gravity coupled to a scalar field. This 1+1 dimensional field theory may be viewed as the ”standard model” for studying black hole physics. Our analysis is adapted to the flat slice Painleve-Gullstrand coordinates. We give a Hamiltonian action principle for this system, which yields an asymptotic mass form...

This paper proposes a method of balanced model reduction for constrained linear port Hamiltonian systems. Constrained linear port Hamiltonian systems are first written in a canonical descriptor form such that the Hamiltonian structure is preserved. The computations of the controllability and observability Gramians are then used to derive the balanced port Hamiltonian representation of the syste...

PACS : 02.30.J, 11.10.E; MSC : 35L65, 35L70, 35Q35, 58F05, 58F07 keywords: Lagrangian, metrics of constant curvature, Hamiltonian structure, reciprocal transformation, Poisson brackets. Abstract. In this article we present a Lagrangian representation for evolutionary systems with a Hamiltonian structure determined by a differential-geometric Poisson bracket of the first order associated with me...

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...

Given a Hamiltonian system, one can represent it using a symplectic map. This symplectic map is specified by a set of homogeneous polynomials which are uniquely determined by the Hamiltonian. In this paper, we construct an invariant norm in the space of homogeneous polynomials of a given degree. This norm is a function of parameters characterizing the original Hamiltonian system. Such a norm ha...

In this paper we show how there is associated an integrable Hamiltonian system to a certain set of algebraic-geometric data. Roughly speaking these data consist of a family of algebraic curves, parametrized by an aane algebraic variety B, a subalgebra C of O(B) and a polynomial '(x; y) in two variables. The phase space is constructed geometrically from the family of curves and has a natural pro...