Gribov Ambiguity

Abstract

Gribov ambiguity is a problem that arises when we try to single out the physical gauge degree of freedom in non-Abelian gauge theory by imposing the covariant gauge constraint. Unfortunately, the solution of the gauge constraint is not unique, thus the redundant gauge degree of freedom, called Gribov copies, remains unfixed. One of the traditional methods to partially resolve the Gribov problem is to restrict the space of gauge orbits inside the bounded region known as the Gribov region. The meaning of "partially resolve" is that this procedure can solve only the positivity's problem of the Faddeev-Popov operator but the Gribov copies are still there. However, on the bright side, the restriction to the Gribov region leads to the modification of the gluon propagator. Additionally, the new form of the gluon propagator yields the violation of the reflection positivity which is considered as the important axiom of the Euclidean quantum field theory. This shows that the gluon field in the Gribov region is an unphysical particle or technically confined. In this review article, we will start by discussing the traditional Faddeev-Popov method and its consequence on the proof of the unitarity of the perturbative Yang-Mills theory. Next, we will discuss the blind spot of the Faddeev-Popov quantization and study the mathematical and physical origin of the Gribov problem. Then, the method of the Gribov restriction will be elaborated. After that, we demonstrate the modification of the gluon field after restricting inside the bounded Gribov region. Finally, we show that the new form of the gluon leads to the violation of the reflection positivity axiom. i I would like to thank Rujikorn Dhanawittayapol, my supervisor, for allowing me to study what I want to. I want to thank my study group's members, especially, Chawakorn Maneerat, Saksilpa Srisukson and Karankorn Kritsarunont for very useful discussions. I also would like to thank my senior, Sirachak Panpanich, for good suggestions. I'm very grateful to give a special thanks to Kei-Ichi Kondo who give many helpful comments on my thesis. Additionally, I also would like to thank Paolo Bertozzini who gives comments on my axiomatic quantum field theory's part of the thesis. In fact, it is very impressive to thank the organizers of the YKIS2018b to let me participate in the conference which makes me found my research interest. Finally, I want to thank Minase Inori, Yura Hatsuki, Ariabl'eyeS, Yurica/Hanatan, =ME and other bands for very wonderful songs when I feel sick about life.