Speaker
Description
Many systems in nature are subjected to thermal effects, i.e., where the environment temperature $T \neq 0$. Likewise, in the presence of conserved charges, chemical potentials can also be present. In this work, we are interested in systems at high temperatures, a condition that prevail in the primordial Universe, and also dense ones, like in the case of compact stars, materials with a well defined chemical potential and candidates for dark mater.
All of those physical systems at $T \neq 0$ share the same problem, the break down of perturbation theory. In other to fix this problem and get access to non-perturbative results, we opitimze our perturbation computations.
There are a few methods of re-summation, that can solve this problem, one in special is the optimized perturbation theory. Instead of expanding our interaction term in the Lagrangian in a Taylor series, we can modify the Taylor expansion itself, multiplying the integrand by some characteristic function. The procedure is quite appropriate for those problems for which the ordinary perturbative expansion does not exhibit dominated convergence.
Applying this technique for the thermal mass and the free energy of a superfluid model (a type Higgs potential) with spontaneous symmetry breaking, we derive essential thermodynamic quantities. In addition, we also have a very accurate correction of the mass spectrum of our theory, since we are in second order in our nonperturbation scheme
(which includes
up to three-loop terms explicitly).
Nowadays, we are developing the same construction for the effective potential, we already done for one, two loops and three loops. In the phase transition analyses there is a puzzle that always came back in literature . This type of theory corresponds to well know class of universality, that have a second order phase transition. However, this is often mislead since we are summing high temperature approximations. Because of this summations, we can be induced to think that perhaps, this type of system undergoes a first-order transition. This can be solved by our proposal using the optimized perturbation theory with the renormalization group equations, we are still developing this correction for high order of perturbation theory.
