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arXiv:1811.05328 · Journal of Physics Conference Series

A new rule for quantization that resolves all problems

John R. Klauder

Published Sep 1, 2019• 1 citation
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Abstract

Abstract While canonical quantization solves many problems there are some problems where it fails. A close examination of the classical/quantum connection leads to a new connection that permits quantum and classical realms to coexist, as is the case in the real world. For those problems for which conventional quantization works well, the new procedures yield identical results. However, we offer an example that fails when quantized conventionally but succeeds when quantized with the new procedures.

DOI
10.1088/1742-6596/1275/1/012003

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Abstract While canonical quantization solves many problems there are some problems where it fails. A close examination of the classical/quantum connection leads to a new connection that permits quantum and classical realms to coexist, as is the case in the real world. For those problems for which conventional quantization works well, the new procedures yield identical results. However, we offer an example that fails when quantized conventionally but succeeds when quantized with the new procedures.
Following Dirac, the rules of canonical quantization include classical and quantum contact transformations of classical and quantum phase space variables. While arbitrary classical canonical coordinate transformations exist that is not the case for some analogous quantum canonical coordinate transformations. This failure is due to the rigid connection of quantum variables arising by promoting the corresponding classical variable from a ccc-number to a qqq-number. A different relationship of ccc-numbers and qqq-numbers in the procedures of Enhanced Quantization shows the compatibility of all quantum operators with all classical canonical coordinate transformations.
Affine quantization is a relatively new procedure, and it can solve many new problems. This essay reviews this new, and novel, procedure for particle problems, as well as those of fields and gravity. New quantization tools, which are extremely close to, and even constructed from, the tools of canonical quantization, are able to fully solve selected problems that using the standard canonical quantization would fail. In particular, improvements can even be found with an affine quantization of fields, as well as gravity.
Canonical quantization is a wonderful procedure for selected problems, but there are many problems for which it fails. Affine quantization is a different procedure that has shown that it can solve many problems that canonical quantization cannot. Here, words like succeed and fail refer to whether the quantization results are correct or incorrect. This paper offers two simple examples that serve to introduce affine quantization, and compare studies of two different quantization procedures. Brief comments about field theory and gravity problems undergoing quantization by affine procedures completes the paper.
Canonical quantization is a wonderful procedure for selected problems, but there are many problems for which it fails. Affine quantization is a different procedure that has shown that it can solve many problems that canonical quantization cannot. Here, words like succeed and fail refer to whether the quantization results are correct or incorrect. This paper offers two simple examples that serve to introduce affine quantization, and compare studies of two different quantization procedures. Brief comments about field theory and gravity problems undergoing quantization by affine procedures completes the paper.