Semantic Foundation of the Quantization Program
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It is a well-known result of VON Neumann  that the representation of the commutation relations of the basic dynamical variables of quantum theory is unique modulo a unitary transformation. This result, valid only for systems having finite numbers of degrees of freedom, seems to imply that, for such mechanical systems, the procedure of quantization is not sensitive to the particular choice of classical canonical variables which one initially employs. This implication is in fact false. The choice of canonical variables which one employs to initiate a quantization of a given classical theory is quite critical.
KeywordsDynamical Variable Unitary Transformation Semantic Content Canonical Transformation Canonical Quantization
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