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

摘要

Based on a perturbative approach, a series expansion in susceptibility function of the medium is obtained for the Casimir force between arbitrarily 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 the weak-coupling regime in the scattering method. The generalization to a massive vector field is also investigated.