The renormalized thermal mass and critical temperature of a complex scalar field theory with non-zero charge density Original Research Article

The linear δ expansion is used to obtain the self-energy up to O(δ2) for a complex scalar field theory with a λ(ϕ★ϕ)2 interaction at high temperature and non-zero chemical potential μ. The calculation is performed in the imaginary-time formalism via the Hamiltonian form of the path integral and non-perturbative results are generated by a systematic order by order variational procedure. The behaviour of the renormalized mass as a function of T and μ is found and the critical temperature extracted. This is plotted as a function of μ and compared with the result of resummed perturbation theory. A detailed calculation of the high-temperature limit of the two-loop “setting-sun” diagram is given, which can easily be adapted to standard perturbation theory.