This book provides a concise description of the current status of a fascinating scientific problem -- the inverse variational problem in classical mechanics. No advanced methods of contemporary differential geometry are used, and all functions are assumed to be piecewise continuous and sufficiently many times differentiable. The book is well suited to be used as lecture notes in a university course for physicists.
This is a set of lecture notes given by the author at the Universities of Gttingen and Wroclaw. The text presents the axiomatic approach to field theory and studies in depth the concepts of symmetry and supersymmetry and their associated generators, currents and charges. It is intended as a one-semester course for graduate students in the field of mathematical physics and high energy physics.
Professor Jerzy Lukierski, an outstanding specialist in the domain of quantum groups, will reach on May 21, 1995 the age of sixty. This is a birthday volume dedicated to him. It assumes the form of a collection of papers on a wide range of topics in modern research area from theoretical high energy physics to mathematical physics. Various topics of quantum groups will be treated with a special emphasis. Quantum groups is nowadays a very fashionable subject both in mathematics and high energy physics.
The present book for the first time links the thoughts of modern Western sociologists of literature with an overall description of the literary activities, attitudes, and views in late eighteenth-century Poland. Inspired by the studies of Bourdieu on literary fields and, more particular, S.J. Schmidt's study of the history of the rise and development of the social system 'literature' in Germany in the eighteenth-century (cf. Schmidt 1989), the author tries to establish whether Poland witnessed the rise of a more complex and (relatively) autonomous literary field or, as Schmidt calls it, a functionally differentiated literary system in the age of the reign of King Stanislaw August Poniatowski (1764-1795). Functionally differentiated literary systems - systems in which an increased number of literary agents and institutions produce, sell, buy, and criticize literary works according to capitalist principles - are the literary systems of today. As most scholars believe, their origins are to be found in most European nations in the late seventeenth and eighteenth centuries. Did such a modern literary system, albeit with certain limitations, rise in Poland in the years of the rule of Stanislaw A. Poniatowski? - this is the question the author of the present volume will attempt to answer. This volume is of interest to theoreticians and empirical researchers approaching literature from a sociological point of view, historians, and, of course, slavists interested in eighteenth-century literary developments in Poland.
This open access book bridges a gap between introductory Quantum Field Theory (QFT) courses and state-of-the-art research in scattering amplitudes. It covers the path from basic definitions of QFT to amplitudes, which are relevant for processes in the Standard Model of particle physics. The book begins with a concise yet self-contained introduction to QFT, including perturbative quantum gravity. It then presents modern methods for calculating scattering amplitudes, focusing on tree-level amplitudes, loop-level integrands and loop integration techniques. These methods help to reveal intriguing relations between gauge and gravity amplitudes and are of increasing importance for obtaining high-precision predictions for collider experiments, such as those at the Large Hadron Collider, as well as for foundational mathematical physics studies in QFT, including recent applications to gravitational wave physics.These course-tested lecture notes include numerous exercises with solutions. Requiring only minimal knowledge of QFT, they are well-suited for MSc and PhD students as a preparation for research projects in theoretical particle physics. They can be used as a one-semester graduate level course, or as a self-study guide for researchers interested in fundamental aspects of quantum field theory.
This book provides a concise description of the current status of a fascinating scientific problem — the inverse variational problem in classical mechanics. The essence of this problem is as follows: one is given a set of equations of motion describing a certain classical mechanical system, and the question to be answered is: Do these equations of motion correspond to some Lagrange function as its Euler-Lagrange equations? In general, not for every system of equations of motion does a Lagrange function exist; it can, however, happen that one may modify the given equations of motion in such a way that they yield the same set of solutions as the original ones and they correspond already to a Lagrange function. Moreover, there can even be infinitely many such Lagrange functions, the relations among which are not trivial. The book deals with this scope of problems. No advanced mathematical methods, such as, contemporary differential geometry, are used. The intention is to meet the standard educational level of a broad group of physicists and mathematicians. The book is well suited for use as lecture notes in a university course for physicists.
This is a set of lecture notes given by the author at the Universities of Gttingen and Wroclaw. The text presents the axiomatic approach to field theory and studies in depth the concepts of symmetry and supersymmetry and their associated generators, currents and charges. It is intended as a one-semester course for graduate students in the field of mathematical physics and high energy physics.
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