2008

Ph.D

HBNI

Quantum Chromo Dynamics is accepted as the theory of strong interaction of quarks and gluons. It is a gauge theory with the gauge group as SU(3)C1 the unbroken color group. In this thesis the author examines the ground state of SU(2) Yang-Mills theory using the background field method, the background being the classical covariantly constant chromomagnetic field in the third colour direction known as the Savvidy Background - first at zero temperature and then at finite temperature. The spontaneous breaking of Global Chiral Symmetry is studied in Chapter V, with pion corrections - using Gribov's approach. Background field method is briefly described in chapter II. The Savvidy background field, a covariantly constant color magnetic field in the third color direction of SU(2) is studied in Chapter III. The one-loop energy density is carefully examined by identifying the stable and unstable modes and evaluating the Matsubara sum and the functional integrals including the cubic and quartic terms for the unstable modes. The study of Savvidy Vacuum is extended in Chapter IV to a finite temperature. A chemical potential for gluons is introduced, originating from the conservation of color charges. The resulting energy density is found to be real and the phase structure of the theory is analyzed it is observed that at high temperatures the behaviour is like that of a relativistic gas. It is shown that the ground state energy of the Savvidy Model is real both at zero and finite temperature.