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

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 transformationTransverse symmetry transformation for BRST symmetry

20. Full Quark-Gluon Vertex Function

24. 6. Outlook