Supplementary conditions in quantized linear systems

A scalar product formalism is presented for the commutation relations and quadratic constants of the motion of a linear system. The modification of commutation relations necessitated by a supplementary operator condition is obtained by means of a projection operation, for which several computational methods are developed; some simple applications are discussed. The foregoing analysis is extended to a sequence of supplementary conditions; it is then applied to quantization of the integral-spin real-meson field.