M. E. Carrington, Wei-Jie Fu
A set of self-consistent nonlinear integral equations for the four-point
vertex and the propagator are derived from the 4-loop 4PI effective action for
scalar field theories. This set of integral equations are solved in two
dimensions through numerical lattice calculations. We compare the calculated
results with those of perturbation theories. We find that the 4PI calculations
are well consistent with the perturbation ones in perturbative regions.
Non-perturbative results are also obtained in the 4PI formalism when the
interacting strength becomes large. Furthermore, the full-momentum dependence
of the four-point vertex is easily obtained in the 4PI effective action
theories.
View original:
http://arxiv.org/abs/1202.3165
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