# Affine Quantization on the Half Line

@article{Gouba2020AffineQO, title={Affine Quantization on the Half Line}, author={Laure Gouba}, journal={arXiv: Quantum Physics}, year={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 method works reasonably well in the case of conventional quantum mechanics over $\mathbb{R}^n$ but it may fail in non-trivial phase spaces and also suffer from ordering problem. Affine quantization is an alternative method, similar to the canonical quantization, that may offer a positive result in…

## 18 Citations

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 Straight Forward Path to a Path Integration of Einstein's Gravity

- Physics
- 2022

Path integration is a respected form of quantization that all the-oretical quantum physicists should welcome. This elaboration begins with simple examples of three diﬀerent versions of path…

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…

The Particle in a Box \Warrants an Examination

- Mathematics
- 2022

The particle in a box is a simple model that has a classical Hamiltonian H = p 2 (using 2 m = 1), with a limited coordinate space, − b < q < b , where 0 < b < ∞ . Using canonical quantization, this…

Vector Affine Quantization Can Create Valid Quantum Field Theories

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

Affine quantization, a parallel procedure to canonical quantization, needs to use its principal quantum operators, specifically ( ) 2 D PQ QP = + and 0 Q ≠ , to represent appropriate kinetic factors,…

0 N ov 2 02 1 Affine Quantization of the Harmonic Oscillator on the Semi-bounded domain ( − b , ∞ ) for b : 0 → ∞

- 2021

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…

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.

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…

Canonical quantization on the half-line and in an interval based upon an alternative concept for the momentum in a space with boundaries

- PhysicsPhysical Review Research
- 2021

For a particle moving on a half-line or in an interval the operator p̂ = −i∂x is not self-adjoint and thus does not qualify as the physical momentum. Consequently canonical quantization based on p̂…

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