Gauge Theories And Two-Dimensional Sigma Models

Abstract

The main purpose of this thesis is studying gauge theories and two-dimensional sigma inodel as a toy-model for testing many phenomena in particle physics, since this model passess similar properties to lour-dimensional non-Abelian gauge theories. Chapter 1, gives a general introduction to the subject. In Chapter 2, we give a brief introduction to the gauge symmetries and gauge theories. The Lagrangian formulatton and the Euler-Lagrange equations are introduced. A discussion of both Abelian and non-Abelian global gauge transformations which imply conservation laws is carried out. Further, we discussed the natural requirement of local phase invariance when imposed on the free fermion Lagrangian which led· to the interacting field theory of quantum electrodynamics (QED ). The consequences of turning non­ .. Abelian glohal symmetry such as· isospin SU(2) into local gauge symmetry and led to Yang-Mills gauge theories. We end this chapter by a critical discussion for the reason why the coworker in this field studying lower dimensional models instead of attacking the problem of non-Abelian gauge theories in four-dimension. In Chapter 3, a detailed discussion of the Euclidean two­ dimensional sigma models is given. Among these models, we start with introducing modelbased on coset spaces, namely, the O(N) 0 models and grassmannian cr models.