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.

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

Canonical quantization (CQ) is built around [Q, P] = iħ1l , while affine quantization (AQ) is built around [Q,D] = iħQ, where D ≡ (PQ +QP) / 2 . The basic CQ operators must fit -∞ < P, Q < ∞ , while the basic AQ operators can fit -∞ < P < ∞ and 0 < Q < ∞ , -∞ < Q < 0 , or even -∞ < Q ≠ 0 < ∞ . AQ can also be the key to quantum gravity, as our simple outline demonstrates.

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.

Affine Quantization on the Half Line

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 Rn but it may fail in non-trivial phase spaces and also suffer from ordering problems. Affine quantization is an alternative method, similar to the canonical quantization, that may offer a positive result in situations for which canonical quantization fails. In this paper we revisit the affine quantization method on the half-line. We formulate and solve some simple models, the free particle and the harmonic oscillator.

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 creates novel tools suitable to eliminate typical difficulties encountered in more conventional approaches.

Vector Affine Quantization Can Create Valid Quantum Field Theories

Affine quantization, a parallel procedure to canonical quantization, needs to use its principal quantum operators, specifically D = (PQ+QP)/2 and Q ≠ 0, to represent appropriate kinetic factors, such as P2, which involves only one canonical quantum operator. The need for this requirement stems from path integral quantizations of selected problems that affine quantization can solve but canonical quantization fails to solve. This task is resolved for simple examples, as well as examples that involve scalar, and vector, quantum field theories.

Using a Toy Model to Improve the Quantization of Gravity and Field Theories

A half-harmonic oscillator, which gets its name because the position coordinate is strictly positive, has been quantized and determined that it was a physically correct quantization. This positive result was found using affine quantization (AQ). The main purpose of this paper is to compare results of this new quantization procedure with those of canonical quantization (CQ). Using Ashtekar-like classical variables and CQ, we quantize the same toy model. While these two quantizations lead to different results, they both would reduce to the same classical Hamiltonian if &hstrok;→ 0. Since these two quantizations have differing results, only one of the quantizations can be physically correct. Two brief sections also illustrate how AQ can correctly help quantum gravity and the quantization of most field theory problems.

Output Feedback Control of Discrete-Time T-S Fuzzy Affine Systems Using Quantized Measurements

This paper investigates the problem of robust H!fixed-order dynamic output feedback( DOF)controller design for a class of Takagi-Sugeno( T-S) fuzzy affine systems using quantized measurements.Through a state-input augmentation method,some sufficient conditions for controller synthesis are developed based upon piecewise quadratic Lyapunov functions( PQLFs) in terms of LMIs. Two illustrative studies are conducted to verify the effectiveness of the proposed controller synthesis approach.

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.

A New Proposal to Create a Valid Quantization of Einstein’s Gravity

Canonical quantization has created many valid quantizations that require infinite-line coordinate variables. However, the half-harmonic oscillator, which is limited to the positive coordinate half, cannot receive a valid canonical quantization because of the reduced coordinate space. Instead, affine quantization, which is a new quantization procedure, has been deliberately designed to handle the quantization of problems with reduced coordinate spaces. Following examples of what affine quantization is, and what it can offer, a remarkably straightforward quantization of Einstein’s gravity is attained, in which a proper treatment of the positive definite metric field of gravity has been secured.

Valid Quantization: The Next Step

Canonical quantization is a wonderful procedure for selected problems, but there are many problems for which it fails. Affine quantization is a different procedure that has shown that it can solve many problems that canonical quantization cannot. Here, words like succeed and fail to refer to whether the quantization results are correct or incorrect. This paper offers two simple examples that serve to introduce affine quantization, and compare studies of two different quantization procedures. Brief comments about field theory and gravity problems undergoing quantization by affine procedures complete the paper.

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 and 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.

A New Proposal for Black Holes

The understanding of what a black hole is like is not easy and may not yet be well understood. The introduction of canonical quantization into the issue has not been significant to our understanding. However, introducing affine quantization, a new procedure, offers a very unusual expression that seems to be plausible, and quite profound as well.

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.

一种基于词袋模型的大规模图像层次化分组算法

大规模图像集合的自动分组,不仅可以帮助用户快速组织和掌握图像集合的内容,并且是基于图像的三维场景重建应用的前提和重要环节。提出一种基于词袋模型(bag-of-words,BOW)的层次化分组算法,将每幅图像表示为一个超高维视词向量,利用多路量化技术将内容相似的图像量化到同一个节点,从而完成对图像粗略分组。然后,在每组类别里面,对图像的局部特征向量进行逐一匹配,并利用仿射空间不变量的约束条件,去除不可靠特征匹配,得到更为准确可靠的图像相似度度量,从而完成图像的精细分组。实验结果表明:从得到的系统不同阶段图像分组的查准率-查全率(precision-recall)曲线可以看出,精细分组过程可以显著提高粗分组精度,并且在精细分组阶段。

压缩数据在SVPN中的一种传输方法

在SVPN中加密传输压缩数据时，为了减少SVPN网关的加密计算量，可以把压缩数据本身分为关键信息和辅助信息两类，只对关键信息进行加密传输。该文讨论了利用SVPN(以IPSec协议为例)分别对这两类信息进行传输的机制。同时还讨论了在几种常见压缩算法中关键信息和辅助信息的具体划分。

基于Tri-training的多特征融合图像检索

为了有效地综合利用图像的多种底层特征进行图像检索,提出将Tri-training方法应用于图像检索过程,将图像的颜色、纹理和形状特征进行了有效的融合。分别提取图像的三维量化颜色直方图、方向可控金字塔二值图像投影和仿射不变区域来表示其颜色、纹理和形状特征,并将三种特征的匹配值作为Tri-training分类器的输入对分类器进行训练和测试。实验结果表明,该方法有效利用了图像的多种特征,达到了很好的检索效果。

基于SIFT特征的小波域数字图像鲁棒水印方法

利用数字图像SIFT(scale invariant feature transform)特征的稳定性和小波变换的特性,提出了一种抗仿射变换和剪切的鲁棒水印算法。水印信息通过量化调制方法嵌在小波变换的低频域。水印检测时,利用匹配的SIFT关键点的位置信息计算仿射变换参数和边缘剪切参数,然后对被检测图像进行逆变换和重定位,恢复水印的同步信息。实验结果表明该算法可以抗击仿射变换和剪切攻击,对常见的图像处理也有很强的鲁棒性。

基于负荷控制潜力量化模型的工业用户群体画像方法

在中国新一轮电力体制改革背景下,研究工业用户负荷参与负荷控制的潜力,对于促进电网安全稳定运行有着积极的作用。以工业用户负荷数据为基础,充分提取用户在不同时间量度下的用电特征,从错时潜力、轮休潜力和避峰潜力3个方面构建多时间尺度负荷控制潜力指标体系。进而将信息熵和逼近理想解排序法相结合,构建负荷控制潜力量化模型,实现了对负荷控制潜力价值的衡量。并且,利用近邻传播算法分析量化模型结果,将用户按照潜力量化值聚类,实现了对不同用户特征群的划分。最后,基于某地区的实际工业用户负荷数据进行算例分析,实现了对工业用户群体负荷控制潜力画像结果的呈现。

基于仿射变换的改进型矢量量化编码

本文提出了基于仿射变换的改进型矢量量化编码算法，并给出了两种不同的实用结构，与传统矢量量化算法相比，该方法在不需要重新训练新码本及不增加码本存储空间的情况下，降低了编码误差，使得重建图像的ＰＳＮＲ显著增加，图像的主观质量也得到很大的改善。