Cluster expansion approach to the effective potential in Φ 4 2+1 -theory

Abstract

We apply a truncated set of dynamical equations of motion for connected equal-time Green functions up to the 4-point level to the investigation of spontaneous ground state symmetry breaking in 4 2+1 quantum eld theory. Within our momentum space discretization we obtain a second order phase transition as soon as the connected 3-point function is included. However, an additional inclusion of the connected 4-point function still shows a signi cant in uence on the shape of the e ective potential and the critical coupling.

Perturbation theory with a variational basis: The generalized Gaussian effective potential

“…Note that unlike of what stated in Ref. [24], the absence of a broken phase is not in contradiction with the analysis by S.F. Magruder [25] and S. Chang and S.F.…”

On three-dimensional coupled bosons

“…As it stands the Hamiltonian would not be a well-defined operator for finite N f theory, we need to introduce mass renormalization terms which correspond in the diagramatic language the setting-sun diagrams [30,31,26]. When we take the large-N f limit these counter terms become of smaller order, therefore the Hamiltonian as written will have a well-defined limit.…”

“…Perturbatively, there is only one type of divergence after normal ordering as we will comment later on [26]. To apply the methods developed by Rajeev, we will use the lightcone coordinates, introduce…”

“…A good review of light-front methods is given in [27], a good discussion of the scalar field in the light-front is also given in [28] and in [29]. The three dimensional scalar field theory has been investigated from different points of view in the articles [30,31,26,32].…”