Related papers: Lagrangian formulation of some q-deformed systems
Quantum superintegrable systems in two dimensions are obtained from their classical counterparts, the quantum integrals of motion being obtained from the corresponding classical integrals by a symmetrization procedure. For each quantum…
In this paper, we introduce a deterministic approach of quantum mechanics for particles with spin 1 2 moving in one dimension. We present a Lagrangian of a spinning particle ($s ={1 \over 2} $), and deduce the expression of the conjugate…
Taking advantage of the flexibility of the variational method with coordinate transformations, we derive a self-consistent set of equations of motion from a discretized Lagrangian to study kinetic plasmas using a Fourier decomposed…
The Hilbert space of a free massless particle moving on a group manifold is studied in details using canonical quantisation. While the simplest model is invariant under a global symmetry, $G \times G$, there is a very natural way to…
We work on some general extensions of the formalism for theories which preserve the relativity of inertial frames with a nonlinear action of the Lorentz transformations on momentum space. Relativistic particle models invariant under the…
The purely affine Lagrangian for linear electrodynamics, that has the form of the Maxwell Lagrangian in which the metric tensor is replaced by the symmetrized Ricci tensor and the electromagnetic field tensor by the tensor of homothetic…
Covariantly we reformulate the description of a spinning particle in terms of the Poincar\'{e} group. We also construct a Lagrangian which entails all possible constraints explicitly; all constraints can be obtained just from the…
It is proposed a Lagrangian for the quasi-rigid extended charged particle, which consists of a bare point particle term plus the standard electromagnetic minimal coupling. The quasi-rigid motion is imposed as a constraint. The extension of…
It is shown that a lagrangian system whose Legendre transformation degenerates along a hypersurface behaves in a strange manner by jumping from time to time without any ''visible cause''. In such a jump the system changes instantaneously…
We study non-conservative like SODEs admitting explicit Lagrangian descriptions. Such systems are equivalent to the system of Lagrange equations of some Lagrangian $L$, including a covariant force field which represents non-conservative…
In quantum field theory the creation and annihilation operators that are located at the points in 3-momentum space have commutation relations that are conserved under the action of a $U({\infty})$ group. Here it is shown how to define an…
We consider classical and quantum mechanics for an extended Heisenberg algebra with additional canonical commutation relations for position and momentum coordinates. In our approach this additional noncommutativity is removed from the…
We study thermodynamics in $f(R)$ gravity with the disformal transformation. The transformation applied to the matter Lagrangian has the form of $\g_{\m\n} = A(\phi,X)g_{\m\n} + B(\phi,X)\pa_\m\f\pa_\n\f$ with the assumption of the…
It is well-known that the equations for a simple fluid can be cast into what is called their Lagrange formulation. We introduce a notion of a generalized Lagrange formulation, which is applicable to a wide variety of systems of partial…
The structure of the Euler-Lagrange equations for a general Lagrangian theory is studied. For these equations we present a reduction procedure to the so-called canonical form. In the canonical form the equations are solved with respect to…
We derive $q$-versions of Green's theorem from the Leibniz rules of partial derivatives for the $q$-deformed Euclidean space. Using these results and the Schr\"{o}dinger equations for a $q$-deformed nonrelativistic particle, we derive…
Symmetries are essential for a consistent formulation of many quantum systems. In this paper we discuss a previously unnoticed symmetry, which is present for any Lagrangian term that involves $\dot{x}^2$. As a basic model that incorporates…
In this article one introduces a formalism of classical mechanics where complex Lagrangian functions are admitted. The results include complex versions of the Lagrangian function, of the Euler-Lagrange equation, of the Hamilton principle, a…
In the q-deformed theory the perturbation approach can be expressed in terms of two pairs of undeformed position and momentum operators. There are two configuration spaces. Correspondingly there are two q-perturbation Hamiltonians, one…
We introduce $q$-versions of the Klein-Gordon equation in the three-dimensional $q$-deformed Euclidean space. We determine plane wave solutions to our $q$-deformed Klein-Gordon equations. We show that these plane wave solutions form a…