نظریه میدان اسکالر کلاسیک با تقارن همدیس و پتانسیل نامثبت

We review the conformal symmetry group and investigate the isomorphism between the conformal group and O( D,2 ) . We study the classically  conformal invariant  scalar theory in D -dimensions with a non-positive potential . We solve the  equations  of motion  by  assigning O(D-1, 2)symmetry to the classical solutions with broken translational symmetry in all directions. Then we consider a six dimensional theory and obtain a set of classical solutions, which are invariant under translation in four out of six directions. We make use of them to construct an effective four dimensional scalar theory induced by the fundamental six dimensional theory. Finally we elaborate the most general solutions of the ø4 massless model in four dimensions.