Quantum Theory of the Electromagnetic Field

Abstract

The electromagnetic field is quantized for free space and for dispersive dielectric media. Different quantum states of the field (thermal, laser, squeezed) are discussed and their photon-statistical properties derived. The density matrix operator for the field is introduced along with a detailed discussion of the diagonal representation of the field density operator and its properties. Field commutation relations, correlation functions, and uncertainty relations are derived and discussed. Also discussed are the historically important Bohr-Rosenfeld analysis of field commutation and uncertainty relations; energy-time uncertainty relations; simultaneous (Arthurs-Kelly) measurement of non-commuting observables; and complementarity from the perspective of probability amplitudes and probabilities for distinguishable and indistinguishable processes.