Tuesday, May 7, 2013

1305.1281 (A. Pallares-Rivera et al.)

Breaking so(4) symmetry without degeneracy lift    [PDF]

A. Pallares-Rivera, F. de J. Rosales-Aldape, M. Kirchbach
On the example of the quantum motion on S3, perturbed by the trigonometric Scarf potential (Scarf I) with one quantized and one continuous parameter, we argue that the breakdown by external scales of a Lie-algebraic symmetry of a quantum system must not necessarily amount to a lift of the degeneracies in the spectrum. To be specific, we show that though the spectrum under discussion carries hydrogen-like degeneracies, the corresponding wave functions do not transform according to so(4) carrier spaces but are finite linear combinations of so(4) representation functions describing carrier spaces of different dimensionality. Alternatively, these decompositions are also expansions in powers of the symmetry breaking scale, and allow to quantitatively describe the order to which the symmetry is violated. We conclude on the general possibility to break perturbatively an intact Lie algebraic symmetry, so(4) in our case, by external scales, such as the continuous parameter of Scarf I, and without leaving trace in the spectra. In effect, degeneracy can throughout be compatible with symmetry breaking.
View original: http://arxiv.org/abs/1305.1281

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