A perturbative approach to calculating the Casimir force in fluctuating scalar and vector fields

Based on a perturbative approach, a series expansion in susceptibility function of the medium is obtained for the Casimir force between arbitrary shaped objects immersed in a scalar or vector fluctuating field in arbitrary dimensions. Finite-temperature corrections are derived and the results are compared in first order with weak coupling regime in scattering method. The generalization to a massive vector field is also investigated.