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HK: Hadronen und Kerne
HK 55: Structure of Baryons, Mesons VIII, Theory
HK 55.1: Group Report
Wednesday, March 18, 1998, 14:00–14:30, J
Symmetry conservation in approximation schemes beyond RPA — •M. Oertel1, M. Buballa1, P. Schuck2, and J. Wambach1 — 1Institut für Kernphysik, Technische Universität Darmstadt — 2Institut des Sciences Nucléaires, Grenoble
A consistent approximation scheme should treat symmetries correctly. It is well known that this is the case for the Hartree-Fock + RPA scheme where spontaneously broken symmetries of the Lagrangian lead to the existence of spurious modes (Goldstone modes). In general this is not true for extensions of the RPA. Starting with the so-called Second RPA (SRPA) we will show that this scheme is not symmetry conserving. As an example we consider the NJL-model where the dynamically broken chiral symmetry implies the existence of massless Goldstone bosons. In standard SRPA the space of possible excitations is restricted to 1q1q and 2q2q degrees of freedom. We show that one has to enlarge this space, such that the conserved charge of the symmetry lies inside this space. From chiral symmetry one also expects the existence of a double excitation of the spurious mode, i.e. two non-interacting Goldstone bosons with zero energy. This requires to work in an even further enlarged space of possible excitations which contains the square of the conserved charge operator. Results and difficulties of this method will be discussed for an explicit example.