  The formalism introduced by Cornwall, Jackiw and Tomboulis (CJT) provides a
systematic approach to consistently resumming non-perturbative effects in
Quantum Thermal Field Theory. One major limitation of the CJT effective action
is that its loopwise expansion introduces residual violations of possible
global symmetries, thus giving rise to massive Goldstone bosons in the
spontaneously broken phase of the theory. In this paper we develop a novel
symmetry-improved CJT formalism for consistently encoding global symmetries in
a loopwise expansion. In our formalism, the extremal solutions of the fields
and propagators to a loopwise truncated CJT effective action are subject to
additional constraints given by the Ward identities due to global symmetries.
By considering a simple O(2) scalar model, we show that, unlike other methods,
our approach satisfies a number of important field-theoretic properties. In
particular, we find that the Goldstone boson resulting from spontaneous
symmetry breaking of O(2) is massless and the phase transition is a second
order one, already in the Hartree-Fock approximation. After taking the sunset
diagrams into account, we show how our approach properly describes the
threshold properties of the massless Goldstone boson and the Higgs particle in
the loops. Finally, assuming minimal modifications to the Hartree-Fock
approximated CJT effective action, we calculate the corresponding
symmetry-improved CJT effective potential and discuss the conditions for its
uniqueness for scalar-field values away from its minimum.
