CONNECTED GREEN-FUNCTION APPROACH TO SYMMETRY-BREAKING IN PHI(4)(1-THEORY(1))

Using the cluster expansions for n-point Green functions we derive a c losed set of dynamical equations of motion for connected equal-time Gr een functions by neglecting all connected functions higher than 4(th) order for the lambda Phi(4)-theory in 1+1 dimensions. We apply the equ ations to the investigation of spontaneous symmetry breaking, i.e. to the evaluation of the effective potential at temperature T = 0. Within our momentum space discretization we obtain a second order phase tran sition (in agreement with the Simon-Griffith theorem) and a critical c oupling of lambda(crit)/4m(2) = 2.446 as compared to a first order pha se transition and lambda(crit)/4m(2) = 2.568 from the Gaussian effecti ve potential approach.