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• W1999836771 abstract "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 dtimes (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 Schrodinger 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 rle 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." @default.
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• W1999836771 date "2001-02-01" @default.
• W1999836771 modified "2023-09-27" @default.
• W1999836771 title "From Gauging Nonrelativistic Translations to N-Body Dynamics" @default.
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• W1999836771 doi "https://doi.org/10.1006/aphy.2000.6120" @default.
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