Quantum Dynamics of a Solvable Nonlinear Chiral Model
197512 pages
Published in:
- J.Phys.A 8 (1975) 1658-1669
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Abstract: (IOP)
The quantum mechanical analogue of a classical nonlinear system is shown to be exactly solvable and its energy levels and eigenfunctions are obtained completely. The symmetric version (k0=0) of this model is the SU(2)(X)SU(2) chiral invariant Lagrangian in the Gasiorowicz-Geffen coordinates. The radial part of the classical equation of motion (in both the symmetric and non-symmetric cases) admits simple harmonic bounded solutions and the bound state energies of the quantized system show a linear dependence on the coupling parameter lambda . It is shown that the Bohr-Sommerfeld quantization procedure reproduces the form of the correct bound state energy levels while a perturbation theoretic treatment gives the exact energy expressions. The ordering problem that arises in the quantum mechanical case is overcome.- QUANTUM MECHANICS
- ENERGY LEVELS
- MODEL: FIELD THEORY
- SYMMETRY: SU(2) X SU(2)
- SYMMETRY: CHIRAL
- PERTURBATION THEORY
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