arXiv subjects
Publications and source records attributed to Per Elmfors.
The QED effective action at finite temperature and density is calculated to all orders in an external homogeneous and time-independent magnetic field in the weak coupling limit. The free energy, obtained explicitly, exhibit the expected de\ Haas -- van\ Alphen oscillations. An effective coupling at finite temperature and density is derived in a closed form and is compared with renormalization group results.
The effective action is computed for the \lphi--theory at finite temperature for small perturbations about a constant background field, using a generalized tadpole method. We find the complete effective action, including the real and imaginary parts, to all orders in derivatives and to order ${\cal O}(λ^2)$. We demonstrate that the high $T$ approximation, where only the zero Matsubara frequency is included, is incorrect for the imaginary part even though it is UV-finite. The solutions of the dispersion relations show that initial perturbations do not necessarily thermalize fast enough to be absent at the onset of phase transition.
The temperature renormalization group equation (TRGE) is compared with a diagrammatic expansion for the $(ϕ^4)_4$-theory. It is found that the one-loop TRGE resums the leading powers of temperature for the effective mass. A two-loop contribution to TRGE is required to do the leading resummation for the coupling constant. It is also shown that the higher order TRGE resums subleading powers of temperature.
A self-consistent renormalization scheme at finite temperature and zero momentum is used together with the finite temperature renormalization group to study the temperature dependence of the mass and the coupling to one-loop order in the $(ϕ^3)_6$- and $(ϕ^4)_4$-models. It is found that the critical temperature is shifted relative to the naive one-loop result and the coupling constants at the critical temperature get large corrections. In the high temperature limit of the $\phiff$-model the coupling decreases.