Source theory of the Casimir force

Abstract

We show how the Casimir force between dielectrics can be calculated in terms of source fields, with no explicit reference to zero-point-field energy. Using Feynman's interpretation of the Lamb shift, the commutativity of equal-time electron and field operators, and a relation between a Green function and a vacuum-field-correlation function, we show why the theories of Lifshitz, van Kampen, and Schwinger produce identical results, even though they appear to be based on very different physical premises. We suggest the possibility of modifying van der Waals-Casimir forces with any external field having some degree of spatial coherence.