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A Smooth Path between the Classical Realm and the Quantum Realm
Authors:John R Klauder
Institution:Department of Physics and Department of Mathematics, University of Florida, Gainesville, FL 32611-8440, USA;
Abstract:A simple example of classical physics may be defined as classical variables, p and q, and quantum physics may be defined as quantum operators, P and Q. The classical world of p&q, as it is currently understood, is truly disconnected from the quantum world, as it is currently understood. The process of quantization, for which there are several procedures, aims to promote a classical issue into a related quantum issue. In order to retain their physical connection, it becomes critical as to how to promote specific classical variables to associated specific quantum variables. This paper, which also serves as a review paper, leads the reader toward specific, but natural, procedures that promise to ensure that the classical and quantum choices are guaranteed a proper physical connection. Moreover, parallel procedures for fields, and even gravity, that connect classical and quantum physical regimes, will be introduced.
Keywords:affine quantization  field theory and gravity  unification of the classical and quantum realms
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