Beyond the Coleman–Weinberg Effective Potential

<!--HTML-->The Two-Particle-Irreducible (2PI) formalism as introduced by Cornwall, Jackiw and Tomboulis provides a systematic analytic approach to consistently describing non-perturbative phenomena in Quantum Field Theory. In spite of its great success, one major problem of the 2PI approach is that its loopwise expansion gives rise to residual violations of symmetries and hence to massive Goldstone bosons in the spontaneously broken phase of the theory. In my talk I will present a novel symmetry-improved 2PI formalism which consistently encodes global symmetries in a loopwise expansion. Unlike other methods, I will illustrate how the symmetry-improved 2PI effective action satisfies a number of important field-theoretic properties, such as the masslessness of the Goldstone boson and the fact that the phase transition is of second order in O(N) theories, already in the Hartree-Fock approximation. After taking the sunset diagrams into account, I show how the symmetry-improved 2PI approach properly describes the threshold properties of the massless Goldstone boson and the Higgs particle within quantum loops. In particular, I will outline the derivation of a symmetry-improved 2PI effective potential, in which new topologies of infinite class of graphs can be resummed that go well beyond the finite-order Coleman--Weinberg effective potential.