15 research outputs found
An Investigation of Singular Lagrangians as Field Systems
The link between the treatment of singular lagrangians as field systems and
the general approch is studied. It is shown that singular Lagrangians as field
systems are always in exact agreement with the general approch.
Two examples and the singular Lagrangian with zero rank Hessian matrix are
studied. The equations of motion in the field systems are equivalent to the
equations which contain accleration, and the constraints are equivalent to the
equations which do not contain acceleration in the general approch treatment.Comment: 10 Pages, Latex, no Figure
Solving conformable Gegenbauer differential equation and exploring its generating function
In this manuscript, we address the resolution of conformable Gegenbauer
differential equations. We demonstrate that our solution aligns precisely with
the results obtained through the power series approach. Furthermore, we delve
into the investigation and validation of various properties and recursive
relationships associated with Gegenbauer functions. Additionally, we introduce
and substantiate the conformable Rodriguez's formula and generating functio
Hamiltonian formulation of systems with linear velocities within Riemann-Liouville fractional derivatives
The link between the treatments of constrained systems with fractional
derivatives by using both Hamiltonian and Lagrangian formulations is studied.
It is shown that both treatments for systems with linear velocities are
equivalent.Comment: 10 page
Hamilton-Jacobi quantization of singular Lagrangians with linear velocities
In this paper, constrained Hamiltonian systems with linear velocities are
investigated by using the Hamilton-Jacobi method. We shall consider the
integrablity conditions on the equations of motion and the action function as
well in order to obtain the path integral quantization of singular Lagrangians
with linear velocities.Comment: late
Bargmann invariants and off-diagonal geometric phases for multi-level quantum systems -- a unitary group approach
We investigate the geometric phases and the Bargmann invariants associated
with a multi-level quantum systems. In particular, we show that a full set of
`gauge-invariant' objects for an -level system consists of geometric
phases and algebraically independent 4-vertex Bargmann
invariants. In the process of establishing this result we develop a canonical
form for U(n) matrices which is useful in its own right. We show that the
recently discovered `off-diagonal' geometric phases [N. Manini and F.
Pistolesi, Phys. Rev. Lett. 8, 3067 (2000)] can be completely analysed in terms
of the basic building blocks developed in this work. This result liberates the
off-diagonal phases from the assumption of adiabaticity used in arriving at
them.Comment: 13 pages, latex, no figure
An investigation of singular Lagrangians as field systems
Consiglio Nazionale delle Ricerche (CNR). Biblioteca Centrale / CNR - Consiglio Nazionale delle RichercheSIGLEITItal