Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2000-07-13
Annals Phys. 288 (2001) 164-196
Physics
High Energy Physics
High Energy Physics - Theory
LaTeX, 38 pages, 1 picture included
Scientific paper
10.1006/aphy.2000.6120
We consider the gauging of space translations with time-dependent gauge functions. Using fixed time gauge of relativistic theory, we consider the gauge-invariant model describing the motion of nonrelativistic particles. When we use gauge-invariant nonrelativistic velocities as independent variables the translation gauge fields enter the equations through a d\times (d+1) matrix of vielbein fields and their Abelian field strengths, which can be identified with the torsion tensors of teleparallel formulation of relativity theory. We consider the planar case (d=2) in some detail, with the assumption that the action for the dreibein fields is given by the translational Chern-Simons term. We fix the asymptotic transformations in such a way that the space part of the metric becomes asymptotically Euclidean. The residual symmetries are (local in time) translations and rigid rotations. We describe the effective interaction of the d=2 N-particle problem and discuss its classical solution for N=2. The phase space Hamiltonian H describing two-body interactions satisfies a nonlinear equation H={\cal H}(\vec x,\vec p;H) which implies, after quantization, a nonstandard form of the Schr\"odinger equation with energy dependent fractional angular momentum eigenvalues. Quantum solutions of the two-body problem are discussed. The bound states with discrete energy levels correspond to a confined classical motion (for the planar distance between two particles r\le r_0) and the scattering states with continuum energy correspond to the classical motion for r>r_0. We extend our considerations by introducing an external constant magnetic field and, for N=2, provide the classical and quantum solutions in the confined and unconfined regimes.
Lukierski Jerzy
Stichel Peter C.
Zakrzewski Wojtek J.
No associations
LandOfFree
From Gauging Nonrelativistic Translations to N-Body Dynamics does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with From Gauging Nonrelativistic Translations to N-Body Dynamics, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and From Gauging Nonrelativistic Translations to N-Body Dynamics will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-415815