Inadmissible axiliary conditions in quantized linear systems

Methods of applying supplementary linear conditions to quantized linear systems are reviewed; it is seen that such a procedure is self-consistent for Fermi-Dirac systems in general, and for Einstein-Bose systems possessing positive definite constants of the motion. Possible modifications are discussed for those cases in which the operator conditions to be added appear intrinsically inconsistent with the commutation relations. Alterations of the commutation relations which maintain the invariance properties of the system are found to be generally inapplicable. Increasing the number of side conditions achieves the desired objective, but at the expense of reducing drastically the class of constants of motion. Finally the introduction of a restricted set of field variables is explored. It is shown that the new variables, in terms of which all pertinent field quantities may be expressed, permit a consistent formulation to be realized; the case of a massless spin s boson field is treated in this manner.