Non-Abelian Stokes Theorem for Wilson Loops Associated with General Gauge Groups

نویسندگان

  • Minoru Hirayama
  • Masataka Ueno
چکیده

A formula constituting the non-Abelian Stokes theorem for general semi-simple compact gauge groups is presented. The formula involves a path integral over a group space and is applicable to Wilson loop variables irrespective of the topology of loops. Some simple expressions analogous to the ’t Hooft tensor of a magnetic monopole are given for the 2-form of interest. A special property in the case of the fundamental representation of the group SU(N) is pointed out.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

ar X iv : h ep - l at / 0 30 90 23 v 1 7 S ep 2 00 3 On the non - Abelian Stokes theorem for SU ( 2 ) gauge fields ITEP - LAT

We derive a version of non-Abelian Stokes theorem for SU(2) gauge fields in which neither additional integration nor surface ordering are required. The path ordering is eliminated by introducing the instantaneous color orientation of the flux. We also derive the non-Abelian Stokes theorem on the lattice and discuss various terms contributing to the trace of the Wilson loop. Introduction The usu...

متن کامل

Non-abelian Stokes Theorem and Quark Confinement in Qcd

To understand the Abelian dominance and magnetic monopole dominance in lowenergy QCD, we rewrite the non-Abelian Wilson loop into the form which is written in terms of its Abelian components or the ’t Hooft-Polyakov tensor describing the magnetic monopole. This is peformed by making use of a version of non-Abelian Stokes theorem. We propose a modified version of the maximal Abelian (MA) gauge. ...

متن کامل

Wilson loop and magnetic monopole through a non-Abelian Stokes theorem

We show that the Wilson loop operator for SU(N) Yang-Mills gauge connection is exactly rewritten in terms of conserved gauge-invariant magnetic and electric currents through a non-Abelian Stokes theorem of the Diakonov-Petrov type. Here the magnetic current originates from the magnetic monopole derived in the gauge-invariant way from the pure Yang–Mills theory even in the absence of the Higgs s...

متن کامل

Non-Abelian Stokes Theorem and Computation of Wilson Loop

It is shown that the application of the non-Abelian Stokes theorem to the computation of the operators constructed with Wilson loop will lead to ambiguity, if the gauge field under consideration is a non-trivial one. This point is illustrated by the specific examples of the computation of a non-local operator. The non-Abelian Stokes theorem is widely applied to compute Wilson loop (closed nonAb...

متن کامل

Non-Abelian Stokes Theorems in Yang–Mills and Gravity Theories

We recall the non-Abelian Stokes theorem for the Wilson loop in the Yang –Mills theory and discuss its meaning. Then we move to ‘gravitational Wilson loops’, i.e. to holonomies in curved d = 2, 3, 4 spaces and derive ‘non-Abelian Stokes theorems’ for these quantities as well, which are similar to our formula in the Yang–Mills theory. In particular we derive an elegant formula for the holonomy i...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 1999