# The Benefits of Affine Quantization

@inproceedings{Klauder2019TheBO, title={The Benefits of Affine Quantization}, author={John Klauder}, year={2019} }

Canonical quantization has served wonderfully for the quantization of a vast number of classical systems. That includes single classical variables, such as p and q, and numerous classical Hamiltonians H(p,q), as well as field theories, such as π(x) and φ(x), and many classical Hamiltonians H(π,φ. However, in all such systems, there are situations for which canonical quantization fails. This includes certain particle and field theory problems. Affine quantization involves a simple recombination…

## 21 Citations

Using Affine Quantization to Analyze Non-Renormalizable Scalar Fields and the Quantization of Einstein’s Gravity

- Physics
- 2020

Affine quantization is a parallel procedure to canonical quantization, which is ideally suited to deal with non-renormalizable scalar models as well as quantum gravity. The basic applications of this…

Affine Quantization on the Half Line

- Physics
- 2020

The similarity between classical and quantum physics is large enough to make an investigation of quantization methods a worthwhile endeavour. As history has shown, Dirac’s canonical quantization…

Solving Major Problems Using Vector Affine Quantization

- MathematicsJournal of High Energy Physics, Gravitation and Cosmology
- 2022

Affine quantization is a parallel procedure to canonical quantization, which is ideally suited to deal with special problems. Vector affine quantization introduces multiple degrees of freedom which…

Affine quantization of
(φ4)4
succeeds while canonical quantization fails

- Mathematics
- 2021

Covariant scalar field quantization, nicknamed ðφÞn, where r denotes the power of the interaction term and n 1⁄4 sþ 1 where s is the spatial dimension and 1 adds time. Models such that r < 2n=ðn − 2Þ…

A COMPARISON BETWEEN CANONICAL QUANTIZATION AND AFFINE QUANTIZATION FOR FIELDS Canonical quantization (CQ) of scalar fields

- Mathematics
- 2021

Following a modest comparison between canonical and affine quantization, which points to positive features in the affine procedures. We prove through Monte Carlo analysis that the covariant euclidean…

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

- Physics
- 2021

Canonical quantization covers a broad class of classical systems, but that does not include all the problems of interest. Affine quantization has the benefit of providing a successful quantization of…

Quantum Gravity, Constant Negative Curvatures, and Black Holes

- Physics
- 2020

For purposes of quantization, classical gravity is normally expressed by canonical variables, namely the metric $g_{ab}(x)$ and the momentum $\pi^{cd}(x)$. Canonical quantization requires a proper…

A Unified Combination of Classical and Quantum Systems

- Physics
- 2020

The goal is to overcome the two separate languages and create a smooth and common procedure that provides a clear and continuous passage between the conventional distinction of either a strictly classical or a strictly quantized state.

The Unification of Classical and Quantum Gravity

- PhysicsJournal of High Energy Physics, Gravitation and Cosmology
- 2021

The favored classical variables that are promoted to quantum operators are divided into three sets that feature constant positive curvatures, constant zero curvatures, as well as constant negative…

Scaled Affine Quantization of $\varphi^4_4$ in the Low Temperature Limit

- Physics
- 2022

We prove through Monte Carlo analysis that the covariant euclidean scalar field theory, φn, where r denotes the power of the interaction term and n = s+ 1 where s is the spatial dimension and 1 adds…

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