Operator ordering and causality beyond the rotating wave approximation

Conventional definition of the time-normal operator ordering (Kelley P. L. and Kleiner W. H., Phys. Rev., 136 (1964) A316) is prone to causality violations (de Haan M., Physica A, 132 (1985) 375; 397). We show that such violations disappear if this definition is amended outside the rotating wave approximation. Nonrelativistic causality of an arbitrary time-normal product turns out to be a property of quantum kinematics, while relativistic causality is demonstrated for a time-normal product of two operators under the most general assumptions about quantum dynamics (commutativity of operators at space-like intervals). This eliminates the key obstacle preventing phase-space techniques of quantum optics from being extended to arbitrary quantum fields including fermions.