Casimir effect in quantum field theory

A new conceptual foundation for renormalizing $T_{\mu \nu }$ on locally flat space-time—to obtain the so-called Casimir effect—is presented. The Casimir ground state is viewed locally as a (nonvacuum) state on Minkowski space-time and the expectation value of the normal-ordered $T_{\mu \nu }$ is taken. The same ideas allow us to treat, for the first time, self-interacting fields for arbitrary mass in perturbation theory—using traditional flat-space-time renormalization theory. First-order results for zero-mass $\lambda {\phi }^4$ theory agree with those recently announced by Ford. We point out the crucial role played by the simple renormalization condition that the vacuum expectation value of $T_{\mu \nu }$ must vanish in Minkowski space-time, and in a critical discussion of other approaches, we clarify the question of renormalization ambiguities for $T_{\mu \nu }$ in curved space-times. In an Appendix, we show how the Casimir effect arises in the $C^{*}$-algebra approach to quantum field theory.