Bose-Einstein condensation temperature of a homogenous weakly interacting Bose gas in variational perturbation theory through seven loops

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 Delta/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 DeltaT(c)/T-0=(1.27+/-0.11)an(1/3). We use seven-loop perturbative coefficients, extending earlier work by one loop order.