场论中高阶微商规范系统的量子对称性质

基于高阶微商规范系统Green函数的生成泛函，导出了该系统在量子水平下的变换性质方程，给出了系统存在量子守恒律的条件和守恒量的表达式．用于高阶微商非Abel Chem—Simons理论，求出了系统的量子BRST守恒荷和其他守恒荷；讨论共形变换下量子水平的变换性质，导出了系统的量子守恒角动量，指出该系统在量子理论中仍可保持分数自旋性质，但经典对称性和守恒律的联系在量子水平不一定再保持．     

Symmetry principles and conservation laws in atomic and subatomic physics — 1

The whole theoretical framework of physics rests only on a few but profound principles. Wigner enlightened us by elucidating that “It is now natural for us to try to derive the laws of nature and to test their validity by means of the laws of invariance, rather than to derive the laws of invariance from what we believe to be the laws of nature.” Issues pertaining to symmetry, invariance principles and fundamental laws challenge the most gifted minds today. These topics require a deep and extensive understanding of both ‘quantum mechanics’ and the ‘theory of relativity’. We attempt in this pedagogical article to present a heuristic understanding of these fascinating relationships based only on rather elementary considerations in classical and quantum mechanics. An introduction to some fundamental considerations regarding continuous symmetries, dynamical symmetries (Part 1), and discrete symmetries (Part 2) (parity, charge conjugation and time-reversal), and their applications in atomic, nuclear and particle physics, will be presented.     

Fermion number fractionization

Solitons emerge as non-perturbative solutions of non-linear wave equations in classical and quantum theories. These are non-dispersive and localised packets of energy — remarkable properties for solutions of non-linear differential equations. In the presence of such objects, the solutions of Dirac equation lead to the curious phenomenon of ‘fractional fermion number’. Under normal conditions the fermion number takes strictly integral values. In this article, we describe this accidental discovery and its manifestation in polyacetylene chains, which has led to the development of organic conductors. (left) Kumar Rao is a Postdoctoral Fellow at PRL, Ahmedabad. He is interested in particle physics phenomenology as probed in particle colliders and formal aspects of quantum field theory. (right) Narendra Sahu is currently a postdoctoral fellow at Lancaster University, UK. His main research area includes Cosmology and Astroparticle physics. Currently he is working on dark matter and matter anti-matter asymmetry of the universe. (center) P K Panigrahi’s research interests are in the area of quantum computation, solitons in Bose Einstein condensates & nonlinear optical media. He is also deeply interested in science education and derives pleasure from long weekend walks.     

量子力学曲率解释与爱因斯坦的非欧线元理论

随着广义相对论的兴起,以及微分几何在物理学中的广泛应用,曲率的概念已经贯穿于理论物理的各大分支.赵国求提出的量子力学曲率解释,不仅有助于协调量子力学与相对论,而且可以帮助人们以更接近广义相对论的思维方式来理解量子规范场论.赵国求认为在弱电统一理论的规范势与广义相对论中的引力势一样,代表着某种空间几何形态的弯曲.爱因斯坦在1927年,就根据赫兹在《力学原理》中的“最小曲率原理”,把薛定谔波动力学原始文献在有关量子波包具有曲率半径的思想,采用广义非欧线元的数学表述,提出了“ψ-曲率张量”的构想,但因为没有把握好深层次的量子关联,即后来玻姆提出的量子势的物理意义而误入歧途.     

Thought Experiments in the Theory of Relativity and in Quantum Mechanics: Their Presence in Textbooks and in Popular Science Books

This work investigates the presence of Thought Experiments (TEs) which refer to the theory of relativity and to quantum mechanics in physics textbooks and in books popularizing physics theories. A further point of investigation is whether TEs – as presented in popular physics books – can be used as an introduction to familiarize secondary school students with physics theories of the 20th century. The study of textbooks and popular physics books showed that authors of both types of books consider TEs as an important tool when presenting the theory of relativity and quantum mechanics. Furthermore, a qualitative research conducted in secondary education revealed that the historical TEs which were transformed into forms accessible to the public could trigger students’ interest and act as educational material to familiarize them with concepts and principles of the 20th century physics.     

三维QED中的动力学手征对称破缺(英文)

为了研究非微扰理论中的传播子行为,以及协变规范对其行为的影响,以常用的截断方案下的DysonSchw inger方程为基础,采用数值联立求解的方法研究了三维量子电动力学(QED)中的费米子和玻色子的行为,并获得了一系列不同规范下费米传播子在Nambu和Wigner相中的自洽解.对这些数值解的分析表明,远离Landau规范的红外区处,传播子行为明显不同于Landau规范中的行为.基于Nambu和Wigner相中的不同规范下的传播子,进一步对等效压力差和费米凝聚随规范参数的变化做了比较,结果表明,采用CJT等效势描述的相变与手征凝聚描述的手征相变两者之间不完全自洽.     

对称性破缺与质量的起源

根据量子规范场理论,阐述对称性破缺机制,揭示了质量产生的根源,肯定了标准模型的重要意义和作用。     

量子真空的哲学问题

量子场是物质的基本形态，量子场论是现代物理学的基本理论，而量子真空正是最低能量状态的量子场，这使得量子真空的研究，成为目前引人注目的自然哲学尖端课题。本文从真空是物质的一种形态、空间度量的断续性、时间度量的断续性、基本作用规律的量子性及统一性、物质结构基元的存在性等五个方面，讨论了当今关于量子真空的本体诠释。     

物理世界相互作用定律的内在不变性——从系统科学哲学视角看规范场论

根据规范场论,自然界各种不同的基本相互作用在实质上都归结为规范场,而“规范对称性”的本质在于“物理定律在变换中保持内在不变性”。按照一般系统论的“不同科学中的同构性”的思想,这种“变换中的不变性”可以推广到包括经济系统和生命系统在内的最一般的系统中去。     

低能光子的量子引力“遗迹”效应

量子引力理论是人类在探索自然界四种基本相互作用统一的道路上的终极目标。其中不少候选理论预言了在低能区的可观测效应,称为量子引力＂遗迹＂效应。本文讨论了量子引力理论对于低能区的光子色散关系的修正,和由此带来的可观测后果,以及现今实验观测上的检验与约束。     

The Heisenberg Microscope: A Powerful Instructional Tool for Promoting Meta-Cognitive and Meta-Scientific Thinking on Quantum Mechanics and the ‚Nature of Science’

In this paper, we present a multi-dimensional study concerning Heisenberg’s ‚gamma ray microscope’, a thought experiment, which is intimately connected with the historical development of quantum mechanics (QM), and also with the most disputed interpretations of quantum theory. In this study: (a) we investigate how philosophers of science read and explicate the function of thought experimentation in physical science; (b) in the light of relevant philosophical theories, we examine the complicated epistemological questions raised by the ‚gamma-ray microscope’ during the birth-process of QM and the contribution of this thought experiment to the clarification of the physical meaning of Heisenberg’s indeterminacy relations; (c) on the basis of the preceding analysis, we propose an instructional intervention, which aims at leading learners not only to an essential understanding of QM worldview, but to a deep insight into the Nature of Science as well.     

Quantum computation

The driving force in the pursuit for quantum computation is the exciting possibility that quantum algorithms can be more efficient than their classical analogues. Research on the subject has unraveled several aspects of how that can happen. Clever quantum algorithms have been discovered in recent years, although not systematically, and the field remains under active investigation. Richard Feynman was one of the pioneers who foresaw the power of quantum computers. In this issue dedicated to him, I give an introduction to how particle and wave aspects contribute to the power of quantum computers. Shor’s and Grover’s algorithms are analysed as examples.     

Symmetry principles and conservation laws in atomic and subatomic physics — 2

This article is the second part of our review of the important role that symmetry plays in atomic and subatomic physics. We will concentrate on the discrete symmetries — parity, charge conjugation, and time reversal — that have played a significant part in the development of the ‘standard model’ of particle physics during the latter part of the 20th century. The importance of experimental tests of these symmetries, in both atomic and particle physics, and their sensitivity to new phenomena is also discussed. To conclude, we describe how ‘symmetry breaking’ in the standard model leads to the generation of mass via the Higgs mechanism and how the search for evidence of this symmetry violation is one of the principal goals of the Large Hadron Collider, which began operating at CERN, Switzerland in 2009.     

Swinging in imaginary time More on the not-so-simple pendulum

When the small angle approximation is not made, the exact solution of the simple pendulum is a Jacobian elliptic function with one real and one imaginary period. Far from being a physically meaningless mathematical curiosity, the second period represents the imaginary time the pendulum takes to swing upwards and tunnel through the potential barrier in the semi-classical WKB approximation¹ in quantum mechanics. The tunneling here provides a simple illustration of similar phenomena in Yang-Mills theories describing weak and strong interactions.     

Ethnicity and student identity in schools: an analysis of official and unofficial talk in multiethnic classrooms

The present study shows that power relations in classrooms between Dutch and immigrant students radically shift when students move from academic talk to more open, free talk. Whereas in their interactions with immigrant students, Dutch students are able to represent the more powerful role in the official, academic discourse, they lose this position in the unofficial, nonacademic discourse. These shifts show that ethnic relationships are played out differently in different discursive domains. They also show that academic identities do not exist as such but are specific to certain minority–majority relationships. This study builds upon a tradition of studies that have argued that ethnic minorities construct academic identities depending on the social setting. However, this study shows the instability of these constructions while demonstrating their dependency on specific ethnic interactions and discursive modes. The study is based on the analysis of interaction patterns in multiethnic classrooms in the Netherlands focussing on (a)symmetries in knowledge sharing. An ethnographic approach is combined with quantitative analyses to test group differences. The results are interpreted and discussed in the light of a poststructuralist view on how ethnic minority groups construct academic identities and how these are related to minority–majority relationships.     

‘Quantum Mechanics’ and ‘Scientific Explanation’ An Explanatory Strategy Aiming at Providing ‘Understanding’

Empirical studies persistently indicate that the usual explanatory strategies used in quantum mechanics (QM) instruction fail, in general, to yield understanding. In this study, we propose an instructional intervention, which: (a) incorporates into its subject matter a critical comparison of QM scientific content with the fundamental epistemological and ontological commitments of the prominent philosophical theories of explanation, a weak form of which we meet in QM teaching; (b) illuminates the reasons of their failure in the quantum domain; and (c) implements an explanatory strategy highly inspired by the epistemological pathways through which, during the birth-process of QM, science has gradually reached understanding. This strategy, an inherent element of which is the meta-cognitive and meta-scientific thinking, aims at leading learners not only to an essential understanding of QM worldview, but to a deep insight into the ‘Nature of Science’ as well.     

Symmetries and conservation laws in classical and quantum mechanics 2. Quantum mechanics

In Part 1 of this two-part article we have spelt out, in some detail, the link between symmetries and conservation principles in the Lagrangian and Hamiltonian formulations of classical mechanics (CM). In this second part, we turn our attention to the corresponding question in quantum mechanics (QM). The generalization we embark upon will proceed in two directions: from the classical formulation to the quantum mechanical one, and from a single (infinitesimal) symmetry to a multi-dimensional Lie group of symmetries. Of course, we always have some definite physical system in mind. We also assume that the reader is familiar with the elements of quantum mechanics at the level of a standard first course on the subject. Operators will be denoted with an overhead caret, e.g., $ \hat A,\hat G,\hat U $ \hat A,\hat G,\hat U , etc., while $ [\hat A,\hat B] = \hat A\hat B - \hat B\hat A $ [\hat A,\hat B] = \hat A\hat B - \hat B\hat A is the commutator of $ \hat A $ \hat A and $ \hat B $ \hat B .     

Quantization of the radiation field

I briefly review the seminal 1927 paper of Dirac which emphasized the need for the quantization of the electromagnetic field and then showed how to carry it out. After mentioning few historical developments, I then point out some of the outstanding successes of quantum electrodynamics —the kind of agreement which exists between theory and experiment is unprecedented in the history of science. Avinash Khare is with the Institute of Physics, Bhubaneswar. His main interests are in the areas of field theory, nonlinear physics, anyons and supersymmetric quantum mechanics.     

Simulated Sustainable Societies: Students’ Reflections on Creating Future Cities in Computer Games

The empirical study, in this article, involved 42 students (ages 14–15), who used the urban simulation computer game SimCity 4 to create models of sustainable future cities. The aim was to explore in what ways the simulated “real” worlds provided by this game could be a potential facilitator for science learning contexts. The topic investigated is in what way interactions in this gaming environment, and reflections about these interactions, can form a context where the students deal with real world problems, and where they can contextualise and apply their scientific knowledge. Focus group interviews and video recordings were used to gather data on students’ reflections on their cities, and on sustainable development. The findings indicate that SimCity 4 actually contributes to creating meaningful educational situations in science classrooms, and that computer games can constitute an important artefact that may facilitate contextualisation and make students’ use of science concepts and theories more explicit.