Chiral Quark Dynamics

These Lecture Notes are based partly on a lecture given by one of us (H. R. ) at Tiibingen University in Spring 1991 and partly on a lecture given at the f Egyptian-German Spring School "Particle and Nuclear Phyic I' in Cairo in April 1992. They are addressed to graduate students and young esearch workers in theoretical physics. Some knowledge ofquantum field theory, especially on func tional integral techniques, are required. These Notes are intended to give a ped agogical introduction into the description of hadrons, Le. , mesons and baryons, within a quark model based on a chirally invariant quantum field theory. A more detailed description of of the subject in Chap. 4, the chiral soliton of the Nambu-Jona-Lasinio model, is given in a recent review [AHW95]. In these Notes we have used results from recent research papers. It is a pleasureto thank our coauthors for their fruitful collaboration. We are especially indebted to Dr. Herbert Weigel who carried the main load in the investigations concerning the NJL soliton. We thank also Albrecht Buck and Udo Ziickert for their valuable contributions. Furthermore we also acknowledge discussions with Kurt Langfeld, Lorenz von Smekal, Christian Weiss, Roman Friedrich, Axel Bender, Gerhard Hellstern, and Jiirgen Schlienz. Tiibingen, January 1995 R. Alkofer H. Reinhardt Contents 1 Introduction 1 2 Reduction of Low-Energy QCD to QFD 5 2. 1 Effective Low-Energy Quark Interaction 5 2. 2 Invariance Properties of QCD and QFD 10 2. 3 Fierz-Transformation ofthe Effective Quark Interaction .

Autorentext
Hugo Reinhardt studierte Physik an der TU Dresden und promovierte am Zentralinstitut für Kernforschung Rossendorf. Nach der Promotion arbeitete er auf dem Gebiet der Kern- und Teilchenphysik in Dubna, Russland und weiterhin in Rossendorf.
Seit 1990 ist er ordentlicher Professor für Theoretische Physik an der Universität Tübingen und ist seit 2006 Direktor des dortigen Instituts für Theoretische Physik.
Hugo Reinhardt war Gastwissenschaftler an renommierten internationalen Instituten, wie z.B. dem Niels-Bohr-Institut Kopenhagen, dem Institut für Theoretische Physik an der Universität von Kalifornien in Santa Barbara und dem MIT Boston.

Klappentext

These notes give an introduction to the description of hadrons, i.e., mesons and baryons, within a quark model based on a chirally invariant quantum field theory. Emphasis is put on a didactic approach intended for graduate students with some background on functional integral techniques. Starting from QCD a motivation of a specific form of the effective quark interaction is given. Functional integral bosonization leads to a theory describing successfully meson properties. It possesses solitonic solutions which are identified as baryons. Via functional integral techniques a Faddeev equation for baryons describing them as bound states of a diquark and a quark is derived. Finally, a unification of these two complementary pictures of baryons is proposed.

Inhalt
Reduction of Low-Energy QCD to QFD.- The Effective Meson Theory.- Baryons as Chiral Solitons.- Baryons as Bound States of Diquarks and Quarks.- On the Description of Baryons: An Outlook.