The QCD Quark Propagator in Coulomb Gauge and - Institut fÃ¼r Physik

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ii Contents 4.6 Numerical results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 5 Meson Observables, Diquark Confinement and Radii 48 6 Nucleon Form Factors in a Covariant Diquark-Quark model 54 6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 6.2 Two-quark correlations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 6.3 Covariant Faddeev equation . . . . . . . . . . . . . . . . . . . . . . . . . . 59 6.3.1 Ansätze for the nucleon and ∆ . . . . . . . . . . . . . . . . . . . . . 59 6.3.2 Propagators and diquark amplitudes . . . . . . . . . . . . . . . . . 62 6.3.3 Solving the Faddeev equation and choices for nucleon and ∆ masses 66 6.4 Electromagnetic current operator . . . . . . . . . . . . . . . . . . . . . . . 67 6.4.1 Coupling to the quark . . . . . . . . . . . . . . . . . . . . . . . . . 69 6.4.2 Coupling to the diquark . . . . . . . . . . . . . . . . . . . . . . . . 70 6.4.3 Coupling to the exchanged quark . . . . . . . . . . . . . . . . . . . 72 6.4.4 Scalar ↔ axialvector transition . . . . . . . . . . . . . . . . . . . . 72 6.4.5 Seagull contributions . . . . . . . . . . . . . . . . . . . . . . . . . . 73 6.5 Nucleon electromagnetic form factors: results . . . . . . . . . . . . . . . . 74 6.5.1 Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 6.5.2 Calculated results and discussion . . . . . . . . . . . . . . . . . . . 75 7 Epilogue 91 A Units and Conventions 93 A.1 Conventions in Minkowski space . . . . . . . . . . . . . . . . . . . . . . . . 93 A.2 Euclidean conventions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 B Gauge potential, field strength and E- and B-fields 95 C Numerical method employed in solving the gap equation with transverse gluons and retardation, eqs. (4.43)-(4.45) 96
Chapter 1 Prologue Quantum Chromo Dynamics (QCD) is the SU(3) gauge theory of quarks and gluons and nowadays the widely accepted theory of strong interaction. Together with the Glashow- Salam-Weinberg Model of electroweak interactions, which succeeded in providing a unified description of the electromagnetic and weak interactions, QCD builds the so-called Standard Model of elementary particle physics. For high momenta, which correspond to small distances, the quarks behave like free particles, a phenomenon which is known as asymptotic freedom. In this momentum regime perturbative calculations have been carried out which agree well with the performed experiments. At low and intermediate momenta up to several GeV however the QCD coupling constant is too large in order to apply perturbation theory. This is physically required since neither quarks nor gluons have been detected as free particles so far. Therefore the confinement hypothesis was established: Only singlets of the gauge group occur as physical particles, which implies that both quarks and gluons should never appear individually. Yet this statement still awaits a rigorous proof. Together with confinement chiral symmetry breaking is the outstanding fundamental low energy property of QCD. Hadron phenomenology, especially the low energy relations in pion physics, the sum rules derived from current algebra and the relations among meson masses left no doubt about the spontaneous breaking of chiral symmetry. Since neither quarks nor gluons can have nonvanishing vacuum expectation values, the breaking of chiral symmetry has to take place dynamically. Our understanding of how observable properties of hadrons emerge from the underlying structure of the strong interaction is still far from complete. Nevertheless in the last years considerable progress has been achieved amongst others in lattice calculations. For example in [D + 04] an unquenched parameterfree calculation for a restricted set of observables testing several aspects of lattice QCD was reported. With u and d quark masses only about three times larger than the realistic value the agreement with experiment was 1
Page 1 and 2: The QCD Quark Propagator in Coulomb
Page 3 and 4: 3 Zusammenfassung In der vorliegend
Page 5: Contents 1 Prologue 1 2 Chiral Symm
Page 9 and 10: Chapter 1. Prologue 3 an ultraviole
Page 11 and 12: Chapter 2 Chiral Symmetry Breaking
Page 13 and 14: Chapter 2. Chiral Symmetry Breaking
Page 21 and 22: Chapter 3 Remarks on QCD in Coulomb
Page 23 and 24: Chapter 3. Remarks on QCD in Coulom
Page 41 and 42: Chapter 4 The Quark Dyson-Schwinger
Page 43 and 44: Chapter 4. The Quark Dyson-Schwinge
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Chapter 5. Meson Observables, Diqua
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Chapter 5. Meson Observables, Diqua
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Chapter 6. Nucleon Form Factors in
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Chapter 7 Epilogue In this thesis w
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Appendix A Units and Conventions In
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Appendix B Gauge potential, field s
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Appendix C. Numerical method employ
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Bibliography 99 [Alk88] Alkofer, Re
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Bibliography 101 [CMZ02] Cucchieri,
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Bibliography 103 [GO03] [GOZ05] [Gr
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Bibliography 105 [Mar04] Maris, Pie
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Bibliography 107 [PS] Peskin, Micha
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The QCD Quark Propagator in Coulomb Gauge and - Institut fÃ¼r Physik

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