Search results for "Free particle"
showing 10 items of 12 documents
Geometric quantization in the presence of an electromagnetic field
1983
Some aspects of the formalism of geometric quantization are described emphasizing the role played by the symmetry group of the quantum system which, for the free particle, turns out to be a central extensionG(m) of the Galilei groupG. The resulting formalism is then applied to the case of a particle interacting with the electromagnetic field, which appears as a necessary modification of the connection 1-form of the quantum bundle when its invariance group is generalized to alocal extension ofG. Finally, the quantization of the electric charge in the presence of a Dirac monopole is also briefly considered.
Direct Evaluation of Path Integrals
2001
Every time τ n is assigned a point y n . We now connect the individual points with a classical path y(τ). y(τ) is not necessarily the (on-shell trajectory) extremum of the classical action. It can be any path between τ n and τn−1 specified by the classical Lagrangian \(L(y,\dot{y},t).\)
Multiscale Particle Method in Solving Partial Differential Equations
2007
A novel approach to meshfree particle methods based on multiresolution analysis is presented. The aim is to obtain numerical solutions for partial differential equations by avoiding the mesh generation and by employing a set of particles arbitrarily placed in problem domain. The elimination of the mesh combined with the properties of dilation and translation of scaling and wavelets functions is particularly suitable for problems governed by hyperbolic partial differential equations with large deformations and high gradients.
Quantization as a consequence of the group law
1982
A method of gemetric quantization which solely makes use of the structure of the symmetry group of the dynamical system is proposed; the classical limit is discussed along similar lines. The method is applied to two examples, the free particle and the harmonic oscillator.
Generalized Conformal Symmetry and Extended Objects from the Free Particle
1998
The algebra of linear and quadratic functions of basic observables on the phase space of either the free particle or the harmonic oscillator possesses a finite-dimensional anomaly. The quantization of these systems outside the critical values of the anomaly leads to a new degree of freedom which shares its internal character with spin, but nevertheless features an infinite number of different states. Both are associated with the transformation properties of wave functions under the Weyl-symplectic group $WSp(6,\Re)$. The physical meaning of this new degree of freedom can be established, with a major scope, only by analysing the quantization of an infinite-dimensional algebra of diffeomorphi…
A Mesh-free Particle Method for Transient Full-wave Simulation
2007
A mesh-free particle method is presented for electromagnetic (EM) transient simulation. The basic idea is to obtain numerical solutions for the partial differential equations describing the EM problem in time domain, by using a set of particles, considered as spatial interpolation points of the field variables, arbitrarily placed in the problem domain and by avoiding the use of a regular mesh. Irregular problems geometry with diffused non-homogeneous media can be modeled only with an initial set of arbitrarily distributed particles. The time dependence is accounted for with an explicit finite difference scheme. Moreover the particle discretization can be improved during the process time ste…
Algebraic Quantization, Good Operators and Fractional Quantum Numbers
1995
The problems arising when quantizing systems with periodic boundary conditions are analysed, in an algebraic (group-) quantization scheme, and the ``failure" of the Ehrenfest theorem is clarified in terms of the already defined notion of {\it good} (and {\it bad}) operators. The analysis of ``constrained" Heisenberg-Weyl groups according to this quantization scheme reveals the possibility for new quantum (fractional) numbers extending those allowed for Chern classes in traditional Geometric Quantization. This study is illustrated with the examples of the free particle on the circumference and the charged particle in a homogeneous magnetic field on the torus, both examples featuring ``anomal…
Singular factorizations, self-adjoint extensions, and applications to quantum many-body physics
2006
We study self-adjoint operators defined by factorizing second order differential operators in first order ones. We discuss examples where such factorizations introduce singular interactions into simple quantum mechanical models like the harmonic oscillator or the free particle on the circle. The generalization of these examples to the many-body case yields quantum models of distinguishable and interacting particles in one dimensions which can be solved explicitly and by simple means. Our considerations lead us to a simple method to construct exactly solvable quantum many-body systems of Calogero-Sutherland type.
Spatial decoherence in QED
2006
We consider the dynamics of a charged free particle, initially described by a coherent wave packet, interacting with an electromagnetic field characterized by the temperature T, considered as the environment. We have used dipole approximation neglecting the potential vector quadratic term in the minimal coupling Hamiltonian. This leads to the loss of coherence in the momentum representation, described by the decay of the off diagonal elements of the particle reduced density matrix, while the populations remain constant. Here we extend the analysis to the coordinate representation. We compute the particle reduced density matrix in this basis, analyzing in particular the mixing of various ef…
Structure of the electromagnetic field around the free electron in nonrelativistic QED.
1991
We study, within the framework of nonrelativistic QED, the structure of the electromagnetic field in the neighborhood of a free spinless electron dressed by the interaction with the vacuum field. We introduce a suitable formalism that correlates electron position and field operators. The quantum average value obtained by applying correlated field operator to the dressed state gives the average value of the corresponding field quantity as a function of distance from the electron. The results obtained separately for the electric- and magnetic-field energy density around the particle display contributions that have quantum origin and that cancel in summing of the two, yielding the total energy…