Quantum Theory of the Electromagnetic Field in a Variable-Length One-Dimensional Cavity

Abstract

The quantum theory of linearly polarized light propagating in a 1-dimensional cavity bounded by moving mirrors is formulated by utilizing the symplectic structure of the space of solutions of the wave equation satisfied by the Coulomb-gauge vector potential. The theory possesses no Hamiltonian and no Schrödinger picture. Photons can be created by the exciting effect of the moving mirrors on the zero-point field energy. A calculation indicates that the number of photons created is immeasurably small for nonrelativistic mirror trajectories and continuous mirror velocities. Automorphic transformations of the wave equation are used to calculate mode functions for the cavity, and adiabatic expansions for these transformations are derived. The electromagnetic field may be coupled to matter by means of a transformation from the interaction picture to the Heisenberg picture; this transformation is generated by an interaction Hamiltonian.