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

@article{Klauder2020UsingAQ, title={Using Affine Quantization to Analyze Non-Renormalizable Scalar Fields and the Quantization of Einstein’s Gravity}, author={John Klauder}, journal={arXiv: General Relativity and Quantum Cosmology}, year={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 approach lead to the common goals of any quantization, such as Schroedinger's representation and Schroedinger's equation. Careful attention is paid toward seeking favored classical variables, which are those that should be promoted to the principal quantum operators. This effort leads toward…

## 12 Citations

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…

Let Loop Quantum Gravity and Affine Quantum Gravity Examine Each Other

- Physics
- 2021

Loop Quantum Gravity is widely developed using canonical quantization in an effort to find the correct quantization for gravity. Affine quantization, which is like canonical quantization augmented…

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…

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…

A Smooth Path between the Classical Realm and the Quantum Realm

- PhysicsEntropy
- 2021

This 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.

Evidence for Expanding Quantum Field Theory

- Physics
- 2021

Present day quantum field theory (QFT) is founded on canonical quantization, which has served quite well, but also has led to several issues. The free field describing a free particle (with no…

Quantum Field Theory Deserves Extra Help

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

Today’s quantum field theory (QFT) relies heavenly on canonical quantization (CQ), which fails for φ4 leading only to a “free” result. Affine quantization (AQ), an alternative quantization procedure,…

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.

Monte Carlo Evaluation of the Continuum Limit of the Two-Point Function of the Euclidean Free Real Scalar Field Subject to Affine Quantization

- MathematicsJournal of Statistical Physics
- 2021

We study canonical and affine versions of the quantized covariant Euclidean free real scalar field-theory on four dimensional lattices through the Monte Carlo method. We calculate the two-point…

A Simple Factor in Canonical Quantization Yields Affine Quantization Even for Quantum Gravity

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

Canonical quantization (CQ) is built around [Q,P ] = ih̄1 , while affine quantization (AQ) is built around [Q,D] = ih̄ Q, where D ≡ (PQ + QP )/2. The basic CQ operators must fit −∞ < P,Q < ∞, while…

## References

SHOWING 1-10 OF 26 REFERENCES

The Benefits of Affine Quantization

- Physics
- 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…

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…

Quantum field theory with no zero-point energy

- Physics
- 2018

A bstractTraditional quantum field theory can lead to enormous zero-point energy, which markedly disagrees with experiment. Unfortunately, this situation is built into conventional canonical…

Enhanced quantization: a primer

- Philosophy
- 2012

Although classical mechanics and quantum mechanics are separate disciplines, we live in a world where Planck’s constant ℏ > 0, meaning that the classical and quantum world views must actually…

Quantum Gravity Made Easy

- Physics
- 2019

Gravity does not naturally fit well with canonical quantization. Affine quantization is an alternative procedure that is similar to canonical quantization but may offer a positive result when…

Background independent quantum gravity: A Status report

- Physics
- 2004

The goal of this review is to present an introduction to loop quantum gravity—a background-independent, non-perturbative approach to the problem of unification of general relativity and quantum…

Canonical Quantum Gravity

- Physics
- 1985

This is a review of the aspirations and disappointments of the canonical quantization of geometry. I compare the two chief ways of looking at canonical gravity, geometrodynamics and connection…

Is Loop Quantum Gravity a Valid Quantization

- Physics
- 2019

Dirac's rule in which only special phase space variables should be promoted to operators in canonical quantization is applied to loop quantum gravity. For this theory, Dirac's rule is violated, and…

Is Loop Quantum Gravity a Physically Correct Quantization?

- Physics
- 2019

Dirac's rule in which only special phase space variables should be promoted to operators in canonical quantization is applied to loop quantum gravity. For this theory, Dirac's rule is violated, and…