Quark Confinement Dynamics

1. Quark Confinement Dynamics 何汉新（Han-Xin He） 中国原子能科学研究院 China Institute of Atomic Energy

2. OUTLINES • 1.Introduction Quark-gluon color confinement Gauge symmetries and QCD Interactions • 2. Transverse symmetry transformations in gauge theories • 3. Transverse Ward-Takahashi relations in QED • 4. Full fermion-boson vertex function in QED • 5. Transverse symmetry transformation and full quark-gluon interaction vertex function

3. 1. Introduction • Quark-gluon color confinement • (1) Confinement mechanism • — A dual Meissner effect in a condensate of magnetic • monopoles • — Hard to prove from QCD • (2) Quark-gluon color confinement dynamics • Lattice QCD simulations • — A linear confinement potential when quark –(anti)quark distance is less than about 1 fm • — String breaking when q-q(anti-quark) distance is larger than 1.1 fm, leading a screen potential • — The dynamic mechanics is still not clear

4. QCD Green’s functions infrared behaviors and color confinement • — Gluon propagator: nearly infrared vanishing • — Ghost propagator: a strongly infrared • enhancing • — To generate a linear arising potential, the quark-quark vertex must be infrared singularity • Problem: how to give the full quark-gluon vertex? • — Only way is to use gauge symmetries in QCD

5. Gauge symmetries --Global: current conservation --Local: Ward-Takahashi relations in QED Slavnov-Taylor relations in QCD • ---Play an essential role in demonstrating the renormalizabilities of gauge theories ---Play the important role in nonperturbative study of gauge theories • The quark-gluon vertex ---is essential for understanding the dynamics of confinement and dynamical chiral symmetry breaking ---plays a key role in bridging color-quarks and gluons and their colorless bound states (hadrons)

9. 2,Transverse Symmetry Transformations in Gauge Theories

10. Physics meaning of the transverse symmetry transformation • The transformation (6) defines a symmetry transformation where the change of variable is along the symmetry direction • The transverse symmetry tranformation (7) transforms the original symmetry direction, by the infinitesimal Lorentz transformation (8), to its tansverse direction. • This is why we call the transformation (7) with definition (8) as the transverse symmetry transformation.

11. 3,Transverse Symmetry Transformation in Abelian Theory QED • We write the transverse symmetry transformation in QED by definition (8)

14. 4. Full Fermion-Boson Vertex Function in QED

16. 5. Transverse Symmetry Transformation in QCD • BRST transformation Transverse symmetry transformation for BRST symmetry

20. Full Quark-Gluon Vertex Function

24. 6. Outlook