We compute the free energy density F for gauge theories, with fermions, at high temperature and zero chemical potential. In the expansion, we determine c ′ 5 and c 5 analytically by calculating two-and three-loop diagrams. The g 5 term constitutes the first correction to the g 3 term and is for the non-Abelian case the last power of g that can be computed within perturbation theory.We find that the g 5 term receives no contributions from overlapping double-frequency sums and that c ′ 5 vanishes.

The renormalization group is used to improve the effective potential of massive O(N) symmetric φ 4 theory. Explicit results are given at the two-loop level.

The free energy of a field theory can be considered as a functional of the free correlation function. As such it obeys a nonlinear functional differential equation which can be turned into a recursion relation. This is solved order by order in the coupling constant to find all connected vacuum diagrams with their proper multiplicities. The procedure is applied to a multicomponent scalar field theory with a φ 4 -self-interaction and then to a theory of two scalar fields φ and A with an interaction φ 2 A. All Feynman diagrams with external lines are obtained from functional derivatives of the connected vacuum diagrams with respect to the free correlation function. Finally, the recursive graphical construction is automatized by computer algebra with the help of a unique matrix notation for the Feynman diagrams.

The shift of the Bose-Einstein condensation temperature for a homogenous weakly interacting Bose gas in leading order in the scattering length a is computed for given particle density n. Variational perturbation theory is used to resum the corresponding perturbative series for ⌬͗ 2 ͘ / Nu in a classical three-dimensional scalar field theory with coupling u and where the physical case of N = 2 field components is generalized to arbitrary N. Our results for N =1,2,4 are in agreement with recent Monte Carlo simulations; for N = 2, we obtain ⌬T c / T 0 = ͑1.27± 0.11͒an 1/3 . We use seven-loop perturbative coefficients, extending earlier work by one loop order.

We predict a novel type of Josephson effect to occur in triplet-superconductor-ferromagnet-triplet-superconductor Josephson junctions. We show that the Josephson current, IJ, exhibits a rich dependence on the relative orientation between the ferromagnetic moment and the d vectors of the superconductors. This dependence can be used to build several types of Josephson current switches. Moreover, we predict an unconventional sign change of IJ with increasing temperature.