We introduce a simple quantum theory of the lossy beam splitter. When applied to describe a Fabry-Pérot cavity this leads to apparently anomalous commutation relations for the intracavity operators. We show that these unfamiliar properties are nevertheless consistent with the fundamental canonical commutator for the vector potential and electric field operators. This result is derived as a consequence of causality as applied to the properties of mirror reflection coefficients.

• Received 15 September 1995

DOI:https://doi.org/10.1103/PhysRevLett.77.1739