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John R. Klauder

Publications and source records attributed to John R. Klauder.

At least 19 recordsLinked to original sources
arXiv2025

Thank The Quantum Realm For Nothing Ever Entering Into Black Holes

While the quantum realm seems hidden, it can also reach examples of infinite energy, especially when a part of space is roughly removed until it disappears, possibly forever. Since it follows that Nothing can enter a region where the space is missing, the quantum realm, as seen now in affine quantization, will automatically come to help everything else by creating colossal `quantum walls' that will ensure that everything stays out of all black holes. In this article, we show that the expanded quantum realm allows Nothing to ever fall into a black hole.

physics.gen-ph↗
arXiv2023

A modest redirection of quantum field theory solves all current problems

Standard quantization using, for example, path integration of field theory models, includes paths of momentum and field reach infinity in the Hamiltonian density, while the Hamiltonian itself remains finite. That fact causes considerable difficulties. In this paper, we represent $π(x)$ by $k(x)/ϕ(x)$. To insure proper values for $π(x)$ it is necessary to restrict $0<|ϕ(x)|<\infty$ as well as $0\leq|k(x)|<\infty$. Indeed that leads to Hamiltonian densities in which $ϕ(x)^p$, where $p$ can be even integers between $4$ and $\infty$. This leads to a completely satisfactory quantization of field theories using situations that involve scaled behavior leading to an unexpected, $\hbar^2/\hatϕ(x)^2$ which arises only in the quantum aspects. Indeed, it is fair to claim that this symbol change leads to valid field theory quantizations.

physics.gen-ph↗
arXiv2023

The Magnificent Realm of Affine Quantization: valid results for particles, fields, and gravity

Affine quantization is a relatively new procedure, and it can solve many new problems. This essay reviews this new, and novel, procedure for particle problems, as well as those of fields and gravity. New quantization tools, which are extremely close to, and even constructed from, the tools of canonical quantization, are able to fully solve selected problems that using the standard canonical quantization would fail. In particular, improvements can even be found with an affine quantization of fields, as well as gravity.

physics.gen-ph↗
arXiv2023

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

Path integration is a respected form of quantization that all theoretical quantum physicists should welcome. This elaboration begins with simple examples of three different versions of path integration. After an important clarification of how gravity can be properly quantized, an appropriate path integral, that also incorporates necessary constraint issues, becomes a proper path integral for gravity that can effectively be obtained. How to evaluate such path integrals is another aspect, but most likely best done by computational efforts including Monte Carlo-like procedures.

gr-qc↗
arXiv2022

Quantum Physics has a New, and Remarkable, Expansion

Canonical quantization has taught us great things. A common example is that of the harmonic oscillator, which is like swinging a ball on a string back and forth. However, the half-harmonic oscillator blocks the ball at the bottom and then it quickly bounces backwards. This second model cannot be correctly solved using canonical quantization. Now, there is an expansion of quantization, called affine quantization, that can correctly solve the half-harmonic oscillator, and offers correct solutions to a grand collection of other problems, which even reaches to field theory and gravity. This paper has been designed to introduce affine quantization; what it is, and what it can do.

quant-ph↗
arXiv2022

Scaled Affine Quantization of Ultralocal $φ^4_2$ a comparative Path Integral Monte Carlo study with Canonical Quantization

After the success of affine quantization in proving through Monte Carlo analysis that the covariant euclidean scalar field theory, $φ^r_n$, where $r$ denotes the power of the interaction term and $n = s + 1$ with $s$ the spatial dimension and $1$ adds imaginary time, such that $r \geq 2n/(n-2)$ can be acceptably quantized and the resulting theory is nontrivial, unlike what happens using canonical quantization, we show here that the same has to be expected for $r>2$ and any $n$ even for the ultralocal field theory. In particular we consider the ultralocal $φ^4_2$ model and study its renormalized properties for both the scaled canonical quantization version and the scaled affine quantization version through path integral Monte Carlo.

hep-th↗
arXiv2022

A Valid Quantization of The Particle in a Box Field Theory, and Well Beyond

The usual particle in a box is turned into a field theory, and its behavior is examined using canonical and affine quantizations. The resulting leads to a valid affine quantization of the particle in a box field theory, which points toward further valid quantizations of more realistic field theory models.

physics.gen-ph↗
arXiv2022

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

We prove through Monte Carlo analysis that the covariant euclidean scalar field theory, $φ^r_n$, where $r$ denotes the power of the interaction term and $n = s + 1$ where $s$ is the spatial dimension and $1$ adds imaginary time, such that $r = n = 4$ can be acceptably quantized using scaled affine quantization and the resulting theory is nontrivial and renormalizable even at low temperatures in the highly quantum regime.

hep-lat↗
arXiv2022

How to Secure Valid Quantizations

Classical mechanics involves position and momentum variables that must be special coordinates chosen to promote to suitable quantum operators. Since classical variables may be broadly chosen, only unique variables should be chosen. We will outline how the favored variables and their suitable quantum operators is guaranteed to assure a truly valid quantization. Invalid quantizations may be mistaken for valid ones, which then leads to incorrect physics. Besides particle examples, there is also a brief run-through for fields and gravity.

physics.gen-ph↗
arXiv2022

Kinetic Factors in Affine Quantization and Their Role in Field Theory Monte Carlo

Affine quantization, which is a parallel procedure with canonical quantization, needs to use its principal quantum operators, most simply $D=(PQ+QP)/2$ and $Q\neq0$, to represent appropriate kinetic factors, normally $P^2$, which involve only one canonical quantum operator. The need for this requirement stems from the quantization of selected problems that require affine quantization to achieve valid Monte Carlo results. This task is resolved for introductory examples as well as examples that involve scalar quantum field theories.

hep-lat↗
arXiv2022

The Particle in a Box Warrants an Examination

The particle in a box is a simple model that has a classical Hamiltonian $H=p^2$ (using $2m=1$), with a limited coordinate space, $-b<q<b$, where $0<b<\infty$. Using canonical quantization, this example has been fully studied thanks to its simplicity, and it is a common example for beginners to understand. Despite its repeated analysis, there is a feature that puts the past results into question. In addition to pointing out the quantization issue, the procedures of affine quantization can lead to a proper quantization that nesaeccsrily points toward more complicated eigenfunctions and eigenvalues, which deserve to be solved.

quant-ph↗
arXiv2022

A Valid Quantization of a Half-Harmonic Oscillator Field Theory

The usual full- and half-harmonic oscillators are turned into field theories, and that behavior is examined using canonical and affine quantization. The result leads to a valid affine quantization of the half harmonic oscillator field theory, which points toward further valid quantizations of more realistic field theory models.

hep-th↗
arXiv2021

Solving Major Problems Using Vector Affine Quantization

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 find that working together create novel tools suitable to eliminate typical difficulties encountered in more conventional approaches.

physics.gen-ph↗
arXiv2021

Monte Carlo evaluation of the continuum limit of the two-point function of the Euclidean free real scalar field subject to affine quantization

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 function at small values of the bare coupling constant and near the continuum limit at finite volume. Our investigation shows that affine quantization is able to give meaningful results for the two-point function for which is not available an exact analytic result and therefore numerical methods are necessary.

hep-lat↗
arXiv2021

Quantum Field Theory Deserves Extra Help

Today's quantum field theory (QFT) relies heavenly on canonical quantization (CQ), which fails for $φ^4_4$ leading only to a "free" result. Affine quantization (AQ), an alternative quantization procedure, leads to a "non-free" result for the same model. Perhaps adding AQ to CQ can improve the quantization of a wide class of problems in QFT.

physics.gen-ph↗
arXiv2021

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

Canonical quantization (CQ) is built around $[Q,P]=i\hbar1\!\!1$, while affine quantization (AQ) is built around $[Q,D]=i\hbar\,Q$, where $D\equiv(PQ+QP)/2$. The basic CQ operators must fit $-\infty< P, Q <\infty$, while the basic AQ operators can fit $-\infty<P<\infty$ and $ 0<Q<\infty$, $-\infty <Q<0$, or even $-\infty<Q\neq0<\infty$. AQ can also be the key to quantum gravity, as our simple outline demonstrates.

gr-qc↗
arXiv2021

Evidence for Expanding Quantum Field Theory

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 interaction term) can suddenly become nonrenormalizable the instant a suitable interaction term appears. For example, using canonical quantization, $φ^4_4$, has been deemed a ``free" theory with no difference from a truly free field [1], [2], [3]. Using the same model, affine quantization has led to a truly interacting theory [4]. This fact alone asserts that canonical and affine tools of quantization deserve to be open to their procedures together as a significant enlargement of QFT.

physics.gen-ph↗