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Canonical quantization covers a broad class of classical systems, but thatdoes not include all the problems of interest. Affine quantization has thebenefit of providing a successful quantization of many important problemsincluding the quantization of half-harmonic oscillators [1] nonrenormalizablescalar fields, such as $(\varphi^{12})_3$ [2], and $(\varphi^4)_4$ [3], as wellas the quantum theory of Einstein's general relativity [4]. The features thatdistinguish affine quantization are emphasized, especially, that affinequantization differs from canonical quantization only by the choice ofclassical variables promoted to quantum operators. Coherent states are used toensure proper quantizations are physically correct. While quantization ofnonrenormalizable covariant scalars and gravity are difficult, we focus onappropriate ultralocal scalars and gravity which are fully soluble while, inthat case, implying that affine quantization is the proper procedure to ensurethe validity of affine quantizations for nonrenormalizable covariant scalarfields and Einstein's gravity.

Using Coherent States to Make Physically Correct Classical-to-Quantum  Procedures that Help Resolve Nonrenomalizable Fields Including Einstein's  Gravity