Volume 119, Number 6, September 2017
|Number of page(s)||6|
|Published online||13 December 2017|
SU(3) gauge theory of nuclear rotations
Department of Physics, Tulane University - New Orleans, LA 70118, USA
Received: 15 October 2017
Accepted: 13 November 2017
The legacy Bohr-Mottelson model of collective rotational modes has a hidden differential geometric structure that enables its natural generalization to a nuclear model that has the mathematical structure of Yang-Mills theory. The essential differential geometry ingredients for Yang-Mills are a base manifold, a gauge group, and a connection or covariant derivative. In this letter, the base manifold is the space of nuclear orientations and quadrupole-monopole deformations, the gauge group is either SO(3) or SU(3), and the covariant derivative determines a new gauge-invariant “magnetic-type” interaction. The high-lying energy states of the legacy irrotational flow model enter, as a direct result of gauge coupling, the domain of low-energy yrast rotational bands, as observed by experiment. Although the relevant SU(3) representation for a deformed nucleus is the same as the Elliott model, the non-Abelian SU(3) gauge group's physical interpretation is very different and concerns the Kelvin circulation.
PACS: 21.60.Fw – Models based on group theory / 02.40.-k – Geometry, differential geometry, and topology / 03.65.Fd – Algebraic methods
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