Areas Of Theoretical Physics Research Articles

Theoretical Physics: A Primer for Philosophers of Science

We give a overview of the main areas in theoretical physics, with emphasis on their relation to Lagrangian formalism in classical mechanics. This review covers classical mechanics; the road from classical mechanics to Schrodinger's quantum mechanics; electromagnetism, special and general relativity, and (very briefly) gauge field theory and the Higgs mechanism. We shun mathematical rigor in favor of a straightforward presentation.

PROFESSOR C. N. YANG AND STATISTICAL MECHANICS

Professor Chen Ning Yang has made seminal and influential contributions in many different areas in theoretical physics. This talk focuses on his contributions in statistical mechanics, a field in which Professor Yang has held a continual interest for over sixty years. His Master's thesis was on the theory of binary alloys with multi-site interactions, some 30 years before others studied the problem. Likewise, his other works opened the door and led to subsequent developments in many areas of modern day statistical mechanics and mathematical physics. He made seminal contributions in a wide array of topics, ranging from the fundamental theory of phase transitions, the Ising model, Heisenberg spin chains, lattice models, and the Yang–Baxter equation, to the emergence of Yangian in quantum groups. These topics and their ramifications will be discussed in this talk.

Robert Harry Kraichnan

Robert Harry Kraichnan

A Unified Grand Tour of Theoretical Physics

Anyone offering a grand tour is faced with several options. Should they concentrate on what may be considered to be essential features, or should they attempt to present a brief glimpse of almost everything? The present offering is a compromise between these two extremes. The area considered - theoretical physics - is now such a vast subject that some kind of compromise is essential. Indeed, the field is now so wide that few could even attempt to review it in a single-authored work. My task here is to assess how well this book has succeeded in its main aim of providing a unified (though introductory) tour of this subject. Constrained within a single volume, this is clearly not an updated Landau-Lifschitz. It cannot be expected to take any particular topic to the level of recent research. Nevertheless, it does seem to cover the broad range of essential topics which now constitute the subject. It starts (most appropriately in my opinion) with geometry. It then covers classical physics, general relativity and quantum theory before moving on to relativistic field theories, statistical mechanics and more modern developments. Naturally, the choice of material to be included in a tour of this kind must depend heavily on the prejudices of the author. These come out very clearly. The book is excellent in its coverage of field theories, but is very weak in areas of condensed-matter physics. This reflects the author's own interests in the early universe. It is therefore likely to please those who are interested in modern approaches to cosmology, and may be approved of by many readers of Classical and Quantum Gravity. However, it is necessary to guard against the impression that this is all there is to theoretical physics. There are deep problems in superconductivity, for example, for which this book provides little preparation. As to level, the depth of coverage is generally greater than that required for most undergraduate programmes, although a specialist undergraduate module may go deeper in some topics. Nevertheless, the breadth is far greater than that usually encountered at this level. The approach to each topic is fairly uniform. A common notation is used consistently, and connections are helpfully indicated between areas that are frequently treated separately. As such, this book is suitable for undergraduates who want a broader view of their subject, for postgraduates who need to catch up quickly in areas they have not previously met, as well as for more experienced researchers who want a brief introduction to topics that are far from their research specialisms. Particularly useful material that has been included in this second edition of the book are introductions to supersymmetry, topological defects and string theory. Although these sections are only introductory, their inclusion represents a significant improvement. There are, however, some eccentricities - for example, the definition of a soliton as a topological defect rather than a solution of a nonlinear equation that is associated with a pole in an associated linear system. Also, there are some naive comments on the philosophy of science in the introduction. But such criticisms are not significant. Within a single volume, this book meets a genuine need. It provides appropriate material to enable many of us to broaden our knowledge into areas that are only loosely related to our own specialisms. I can certainly recommend it, and I am sure I will regularly use it personally. The author should be congratulated on generally meeting the aims he set out to achieve, at least within field theory areas of theoretical physics. It is likely to prove to be an extremely helpful resource.

Julian Schwinger: The Physicist, the Teacher and the Man

In the post-quantum-mechanics era, few physicists, if any, have matched Julian Schwinger in contributions to and influence on the development of physics. A deep and provocative thinker, Schwinger left his indelible mark on all areas of theoretical physics; an eloquent lecturer and immensely successful mentor, he was gentle, intensely private, and known for being “modest about everything except his physics”. This book is a collection of talks in memory of him by some of his contemporaries and his former students: A Klein, F Dyson, B DeWitt, W Kohn, D Saxon, P C Martin, K Johnson, S Deser, R Finkelstein, Y J Ng, H Feshbach, L Brown, S Glashow, K A Milton, and C N Yang. From it, one can get a glimpse of Julian Schwinger, the physicist, the teacher, and the man. Altogether, this book is a must for all physicists, physics students, and others who are interested in great legends.

Julian Schwinger: Prodigy, Problem Solver, Pioneering Physicist

Most theoretical physicists rely on interactions with others to stay abreast of theoretical and experimental advances. In classrooms and seminars, on blackboards and napkins, they exchange and clarify ideas with colleagues and students. Rare is the theoretical physicist who makes repeated and varied contributions apart from the throng; rarer still is one who not only contributes but also sets standards and priorities singlehandedly. Julian Seymour Schwinger, who died 16 July 1994 at the age of 76, was such an individual. Gentle but steadfastly independent, quiet but dramatically eloquent, self‐taught and self‐propelled, brilliant and prolific, Schwinger remained active and productive until his death. His ideas, discoveries and techniques pervade all areas of theoretical physics.

REMINISCENCES ABOUT MANY PITFALLS AND SOME SUCCESSES OF QFT WITHIN THE LAST THREE DECADES

Laymen and sometimes even physicists think of natural sciences, in particular of theoretical and mathematical physics often as subjects, which unfold according to an intrinsic logical pattern, with the limitations being set only by the conceptual and (in case of mathematical physics) mathematical developments of the times. This view certainly cannot be maintained in view of the present stagnation and crisis which in particular affects QFT, an area which in the past has been most innovating and fruitful, also in relation to other important areas of theoretical physics.

A nonlinear elliptic equation arising from gauge field theory and cosmology

We study radially symmetric solutions of a nonlinear elliptic partial differential equation in R 2 with critical Sobolev growth, i. e. the nonlinearity is of exponential type. This problem arises from a wide variety of important areas in theoretical physics including superconductivity and cosmology. Our results lead to many interesting implications for the physical problems considered. For example, for the self-dual Chern–Simons theory, we are able to conclude that the electric charge, magnetic flux, or energy of a non-topological N -vortex solution may assume any prescribed value above an explicit lower bound. For the Einstein-matter-gauge equations, we find a necessary and sufficient condition for the existence of a self-dual cosmic string solution. Such a condition imposes an obstruction for the winding number of a string in terms of the universal gravitational constant.

Superstring theory: Information transfer in an emerging field

This paper traced an individual paper through the literature as it garnered citations. This paper was chosen because of its seminal nature in a highly controversial area of theoretical physics. The distribution of citations was tested against models suggested byPrice andKuhn as well as compared to other studies which also examined benchmark papers. The results indicate that the paper chosen behaved in a significantly different way from most of the prior models. The suggestion is made that further study of this and papers like it will add much to the theory of information transfer in science.

Finite element modelling of weak plasma turbulence

The quasilinear theory, the lowest order nonlinear theory of plasma turbulence is nowadays one of the most consolidated and useful theoretical tools for the investigation of several important problems in the domain of controlled nuclear fusion research. Perhaps, the best merit of quasilinear theory is that of reducing the complicated phenomenon of the wave-particle interaction within the familiar framework of advection-diffusion processes for which a huge amount of wisdom can be straightforwardly imported from other areas of theoretical physics. A recent application where quasilinear theory has been successfully applied concerns the study of lower hybrid current drive, i.e., the description of the mechanisms by which a steady current can be maintained in thermonuclear plasmas by injecting electromagnetic waves from the exterior with no assist of any applied ohmic voltage or even in opposition to it. In this paper we describe the main features associated with the implementation of the quasilinear model of lower hybrid current drive into a numberical code. Our study is based on ADLER, a finite element code designed to solve the quasilinear equations in two dimensions in velocity and wave number space. Special attention is paid to the algebraic solver, which was found to be the computationally most intensive section of the code. In particular we have compared the direct Gauss elimination technique with a series of vectorized iterative solvers developed at ECSEC. This comparison shows that the iterative solvers do perform successfully and, apart from the obvious savings of storage, they also prove advantageous from the viewpoint of CPU costs especially when the grid resolution is augmented. Finally, some new application of ADLER in the domain of unsteady lower hybrid current drive are presented. A good qualitative agreement with the experimental result is found, showing once more that quasilinear theory is an appropriate tool for the description of the current drive physics.

Painless nonorthogonal expansions

In a Hilbert space ℋ, discrete families of vectors {hj} with the property that f=∑j〈hj‖ f〉hj for every f in ℋ are considered. This expansion formula is obviously true if the family is an orthonormal basis of ℋ, but also can hold in situations where the hj are not mutually orthogonal and are ‘‘overcomplete.’’ The two classes of examples studied here are (i) appropriate sets of Weyl–Heisenberg coherent states, based on certain (non-Gaussian) fiducial vectors, and (ii) analogous families of affine coherent states. It is believed, that such ‘‘quasiorthogonal expansions’’ will be a useful tool in many areas of theoretical physics and applied mathematics.

Properties of isolated singularities of some functions taking values in real Clifford algebras

The study of solutions to special examples of elliptic differential equations, using Clifford algebras, has been developed by a number of authors [4–12, 14–16, 18, 19, 21–30, 32]. This study has also been applied [3, 13, 17, 28] within a number of areas of theoretical physics, including Yang–Mills field theory, and the Kähler equation. Most of the function theories associated to the solutions of these elliptic differential equations, referred to as generalized Cauchy–Riemann equations [21,32], generalize in a natural manner many aspects of classical one-variable complex analysis [1]. For instance, each of these function theories contain analogues of the Cauchy theorem, Cauchy integral formula and Laurent expansion theorem. However, no information has yet been obtained on the local topological behaviour of a general solution to any of these equations.

Applications of catastrophe theory to the physical sciences

Catastrophe Theory was introduced by René Thom in the late 1960's, as an attempt to model morphogentic changes in nature using ideas from topological dynamics and the theory of singularities of mappings. Thom envisaged a very general approach to topological changes in the solutions to parametrized systems of equations (such as differential and difference equations), and in particular discussed the special case of ‘elementary’ catastrophe theory: singularities of smooth real-valued functions. Popular expositions have tended to overemphasize this special case, but it remains the major source of ideas and methods. Here we survey the applications of Catastrophe Theory to the physical sciences (physics, chemistry, engineering, fluid mechanics, etc.). For brevity we confine attention to an area lying between ‘elementary’ and ‘general’ Catastrophe Theory, usually known as Singularity Theory. This is the theory of singularities of smooth vector-valued functions, which mathematically is a straightforward (though non-trivial) generalization of the real-valued case. In the last few years it has developed into a powerful and useful technique in several areas of theoretical physics, notably optics and bifurcation theory. Equivariant Catastrophe Theory, taking account of symmetry, is likely to prove especially interesting.