The quantum theory of a massless free field in a one-dimensional cavity bounded by moving mirrors is formulated in terms of an effective Hamiltonian density which is defined over a fixed length. This effective Hamiltonian is obtained from the original Hamiltonian by the application of a unitary time-dependent transformation with the property that it preserves the reciprocal symmetry of the free field. Using this formulation, the number and the spectrum of the excitations created by the action of the moving mirror on the zero-point energy of the cavity is found in first-order perturbation theory.

• Received 6 August 1984

DOI:https://doi.org/10.1103/PhysRevD.31.307