On the s-parameterized Quantization Scheme for Dirac’s Representation theory

Abstract

Dirac is the founder of quantum mechanical representation theory. By virtue of the technique of integration within an ordered product (IWOP) of operators we introduce s-parameterized form of quantum mechanical coordinate and momentum representations, which are complete. We then point out that s-parameterized representation’s completeness relation is accompanied with operators’ s-ordering, the special cases s=1,0,−1 correspond to normal-ordering, Weyl ordering and antinormal-ordering, respectively. The s-parameterized form of the coherent state representation and the entangled state representation are also derived. In our view, the operators’ s-ordering should be traced back to s-parameterized form of the completeness relation of quantum mechanical coordinate and momentum representations, which is more fundamental. Many operator identities can be derived by virtue of the above mentioned s-parameterized representation’s completeness relations.