  The principles of the electromagnetic fluctuation-induced phenomena such as
Casimir forces are well understood. However, recent experimental advances
require universal and efficient methods to compute these forces. While several
approaches have been proposed in the literature, their connection is often not
entirely clear, and some of them have been introduced as purely numerical
techniques. Here we present a unifying approach for the Casimir force and free
energy that builds on both the Maxwell stress tensor and path integral
quantization. The result is presented in terms of either bulk or surface
operators that describe corresponding current fluctuations. Our surface
approach yields a novel formula for the Casimir free energy. The path integral
is presented both within a Lagrange and Hamiltonian formulation yielding
different surface operators and expressions for the free energy that are
equivalent. We compare our approaches to previously developed numerical methods
and the scattering approach. The practical application of our methods is
exemplified by the derivation of the Lifshitz formula.
