arXiv subjects

John R. Klauder

Publications and source records attributed to John R. Klauder.

At least 37 records · Page 2Linked to original sources

arXiv2021

Let Loop Quantum Gravity and Affine Quantum Gravity Examine Each Other

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 bounded in one orientation, e.g., a strictly positive coordinate. We open discussion using canonical and affine quantizations for two simple problems so each procedure can be understood. That analysis opens a modest treatment of quantum gravity gleaned from some typical features that exhibit the profound differences between aspects of seeking the quantum treatment of Einstein's gravity.

gr-qc↗

arXiv2021

Is Loop Quantum Gravity a Physically Correct Quantization?

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 as a result loop quantum gravity fails the test to be a valid quantization. Indications are included on how to create and deal with valid versions of quantum gravity.

physics.gen-ph↗

arXiv2021

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

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 many important problems including the quantization of half-harmonic oscillators [1] nonrenormalizable scalar fields, such as $(φ^{12})_3$ [2], and $(φ^4)_4$ [3], as well as the quantum theory of Einstein's general relativity [4]. The features that distinguish affine quantization are emphasized, especially, that affine quantization differs from canonical quantization only by the choice of classical variables promoted to quantum operators. Coherent states are used to ensure proper quantizations are physically correct. While quantization of nonrenormalizable covariant scalars and gravity are difficult, we focus on appropriate ultralocal scalars and gravity which are fully soluble while, in that case, implying that affine quantization is the proper procedure to ensure the validity of affine quantizations for nonrenormalizable covariant scalar fields and Einstein's gravity.

physics.gen-ph↗

arXiv2020

The Unification of Classical and Quantum Gravity

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 curvatures. This list covers the spin variables, the canonical variables, and the affine variables, and these three topics will be briefly reviewed. In this discussion, appropriate coherent states are introduced which are the principal items that are critical in the unification of relevant classical and quantum realms. This analysis can also serve to unify classical gravity and quantum gravity without any speculative aspects..

physics.gen-ph↗

arXiv2020

A Unified Combination of Classical and Quantum Systems

Any particular classical system and its quantum version are normally viewed as separate formulations that are strictly distinct. Our 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. While path integration, among other procedures, provides an alternative route to connect classical and quantum expressions, it normally involves complicated, model-dependent, integrations. Our alternative procedures involve only model-independent procedures, and use more natural and straightforward integrations that are universal in kind. To introduce the basic procedures our presentation begins with familiar methods that are limited to basic, conventional, canonical quantum mechanical examples. In the final sections we illustrate how alternative quantization procedures, e.g., spin and affine quantizations, can also have smooth paths between classical and quantum stories, and with a few brief remarks, can also lead to similar stories for non-renormalizable covariant scalar fields as well as quantum gravity.

quant-ph↗

arXiv2020

An Ultralocal Classical and Quantum Gravity Theory

An ultralocal form of any classical field theory eliminates all spatial derivatives in its action functional, e.g., in its Hamiltonian functional density. It has been applied to covariant scalar field theories and even to Einstein's general relativity, by Pilati, as an initial term in a perturbation series that aimed to restore all omitted derivatives. Previously, the author has quantized ultralocal scalar fields by affine quantization to show that these non-renormalizanle theories can be correctly quantized by affine quantization; the story of such scalar models is discussed in this paper. The present paper will also show that ultralocal gravity can be successfully quantized by affine quantization. The purpose of this study is that a successful affine quantization of any ultralocal field problem implies that, with properly restored derivatives, the classical theory can, in principle, be guaranteed a successful result using either a canonical quantization or an affine quantization. In particular, Einstein's gravity requires an affine quantization, and it will be successful.

gr-qc↗

arXiv2020

The Favored Classical Variables to Promote to Quantum Operators

Classical phase-space variables are normally chosen to promote to quantum operators in order to quantize a given classical system. While classical variables can exploit coordinate transformations to address the same problem, only one set of quantum operators to address the same problem can give the correct analysis. Such a choice leads to the need to find the favored classical variables in order to achieve a valid quantization. This article addresses the task of how such favored variables are found that can be used to properly solve a given quantum system. Examples, such as non-renormalizable scalar fields and gravity, have profited by initially changing which classical variables to promote to quantum operators.

hep-th↗

arXiv2020

Using Affine Quantization to Analyze Non-renormalizable Scalar Fields and the Quantization of Einstein's Gravity

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 classical variables that have a constant positive, zero, or negative curvature, which typically characterize such favored variables. This focus leans heavily toward affine variables with a constant negative curvature, which leads to a surprisingly accommodating analysis of non-renormalizable scalar models as well as Einstein's general relativity.

gr-qc↗

arXiv2020

Quantum Gravity, Constant Negative Curvatures, and Black Holes

For purposes of quantization, classical gravity is normally expressed by canonical variables, namely the metric $g_{ab}(x)$ and the momentum $π^{cd}(x)$. Canonical quantization requires a proper promotion of these classical variables to quantum operators, which, according to Dirac, the favored operators should be those arising from classical variables that formed Cartesian coordinates; sadly, in this case, that is not possible. However, an affine quantization features promoting the metric $g_{ab}(x)$ and the momentric $π^c_d(x)\;[\equiv π^{ce}(x) \,g_{de}(x)]$ to operators. Instead of these classical variables belonging to a constant zero curvature space (i.e., instead of a flat space), they belong to a space of constant negative curvatures. This feature may even have its appearance in black holes, which could strongly point toward an affine quantization approach to quantize gravity.

gr-qc↗

arXiv2019

The Benefits of Affine Quantization

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 of classical variables that lead to a new chapter in the process of quantization, and which is able to solve a vast variety of normally insoluble systems, such as quartic interactions in scalar field theory in spacetime dimensions 4 and higher, as well as the quantization of Einstein's gravity in 4 spacetime dimensions.

physics.gen-ph↗

arXiv2019

Quantum Gravity Made Easy

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 canonical quantization fails to offer a positive result. Two simple examples given initially illustrate the power of affine quantization. These examples clearly point toward an affine quantization procedure that vastly simplifies a successful quantization of general relativity.

gr-qc↗

arXiv2019

Building a Genuine Quantum Gravity

An affine quantization approach leads to a genuine quantum theory of general relativity by extracting insights from a short list of increasingly more complex, soluble, perturbably nonrenormalizable models.

gr-qc↗

arXiv2018

Solving the Insoluble: A New Rule for Quantization

The rules of canonical quantization normally offer good results, but sometimes they fail, e.g., leading to quantum triviality ($=$ free) for certain examples that are classically nontrivial ($\ne$ free). A new procedure, called Enhanced Quantization, relates classical models with their quantum partners differently and leads to satisfactory results for all systems. This paper features enhanced quantization procedures and provides highlights of two examples, a rotationally symmetric model and an ultralocal scalar model, for which canonical quantization fails while enhanced quantization succeeds.

quant-ph↗

arXiv2018

A New Rule for Quantization that Resolves All Problems

While canonical quantization solves many problems there are some problems where it fails. A close examination of the classical/quantum connection leads to a new connection that permits quantum and classical realms to coexist, as is the case in the real world. For those problems for which conventional quantization works well, the new procedures yield identical results. However, we offer an example that fails when quantized conventionally but succeeds when quantized with the new procedures.

quant-ph↗

arXiv2018

Quantum Field Theory With No Zero-Point Energy

Traditional quantum field theory can lead to enormous zero-point energy, which markedly disagrees with experiment. Unfortunately, this situation is built into conventional canonical quantization procedures. For identical classical theories, an alternative quantization procedure, called affine field quantization, leads to the desirable feature of having a vanishing zero-point energy. This procedure has been applied to renormalizable and nonrenormalizable covariant scalar fields, fermion fields, as well as general relativity. Simpler models are offered as an introduction to affine field quantization.

hep-th↗

arXiv2017

Enhanced Quantization: The Right way to Quantize Everything

Canonical quantization relies on Cartesian, canonical, phase-space coordinates to promote to Hermitian operators, which also become the principal ingredients in the quantum Hamiltonian. While generally appropriate, this procedure can also fail, e.g., for covariant, quartic, scalar fields in five-and-more spacetime dimensions (and possibly four spacetime dimensions as well), which become trivial; such failures are normally blamed on the `problem' rather than on the 'quantization procedure'. In Enhanced Quantization the association of $c$-numbers to $q$-numbers is chosen very differently such that: (i) there is no need to seek classical, Cartesian, phase-space coordinates; (ii) every classical, contact transformation is applicable and no change of the quantum operators arises; (iii) a new understanding of the importance of 'Cartesian coordinates' is established; and (iv) although discussed elsewhere in detail, the procedures of enhanced quantization offer fully acceptable solutions yielding non-trivial results for quartic scalar fields in four-and-more spacetime dimensions. In early sections, this paper offers a wide-audience approach to the basic principles of Enhanced Quantization using simple examples; later, several significant examples are cited for a deeper understanding. An historical note concludes the paper.

quant-ph↗

arXiv2017

Mixed Models: Combining Incompatible Scalar Models in Any Spacetime Dimension

Traditionally, covariant scalar field theory models are either super renormalizable, strictly renormalizable, or nonrenormalizable. The goal of `Mixed Models' is to make sense of sums of these distinct examples, e.g., $gφ^4_3+g'φ^6_3+g''φ^8_3$, which includes an example of each kind for spacetime dimension $n=3$. We show how the several interactions such mixed models have may be turned on and off in any order without any difficulties. Analogous results are shown for $gφ^4_n+g'φ^{138}_n$, etc., for all $n\ge3$. Different categories hold for $n=2$ such as, e.g., ${g P(φ)_2+g' N\!P}(φ)_2$, that involve polynomial ($P$) and suitable nonpolynomial ($N\!P$) interactions, etc. Analogous situations for $n=1$ (time alone) offer simple `toy' examples of how such mixed models may be constructed.

hep-th↗

arXiv2017

Do spikes persist in a quantum treatment of spacetime singularities?

The classical approach to spacetime singularities leads to a simplified dynamics in which spatial derivatives become unimportant compared to time derivatives, and thus each spatial point essentially becomes uncoupled from its neighbors. This uncoupled dynamics leads to sharp features (called "spikes") as follows: particular spatial points follow an exceptional dynamical path that differs from that of their neighbors, with the consequence that, in the neighborhood of these exceptional points, the spatial profile becomes ever more sharp. Spikes are consequences of the BKL-type oscillatory evolution towards generic singularities of spacetime. Do spikes persist when the spacetime dynamics is treated using quantum mechanics? To address this question, we treat a Hamiltonian system that describes the dynamics of the approach to the singularity and consider how to quantize that system. We argue that this particular system is best treated using an affine quantization approach (rather than the more familiar methods of canonical quantization) and we set up the formalism needed for this treatment. Our investigation, based on this affine approach, shows the nonexistence of quantum spikes.

gr-qc↗