2021/04/28 by John R. Klauder, Klauder, John R.
Physics and Astronomy · #Atomic and Subatomic Physics Research #Cosmology and Gravitation Theories #FOS: Physical sciences #General Physics (physics.gen-ph) #Quantum Mechanics and Applications
paper · pdf · doi:10.48550/arxiv.2105.03206
openalex publication_date 2021/04/28 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28
Canonical quantization covers a broad class of classical systems, but that\ndoes not include all the problems of interest. Affine quantization has the\nbenefit of providing a successful quantization of many important problems\nincluding the quantization of half-harmonic oscillators [1] nonrenormalizable\nscalar fields, such as (\φ12)3 [2], and (\φ4)4 [3], as well\nas the quantum theory of Einstein's general relativity [4]. The features that\ndistinguish affine quantization are emphasized, especially, that affine\nquantization differs from canonical quantization only by the choice of\nclassical variables promoted to quantum operators. Coherent states are used to\nensure proper quantizations are physically correct. While quantization of\nnonrenormalizable covariant scalars and gravity are difficult, we focus on\nappropriate ultralocal scalars and gravity which are fully soluble while, in\nthat case, implying that affine quantization is the proper procedure to ensure\nthe validity of affine quantizations for nonrenormalizable covariant scalar\nfields and Einstein's gravity.\n