Download or read book Combinatorial Physics written by Adrian Tanasa and published by Oxford University Press. This book was released on 2021 with total page 409 pages. Available in PDF, EPUB and Kindle. Book excerpt: The goal of the book is to use combinatorial techniques to solve fundamental physics problems, and vice-versa, to use theoretical physics techniques to solve combinatorial problems.
Download or read book Combinatorial Physics written by Adrian Tanasa and published by Oxford University Press. This book was released on 2021-04-16 with total page 420 pages. Available in PDF, EPUB and Kindle. Book excerpt: The interplay between combinatorics and theoretical physics is a recent trend which appears to us as particularly natural, since the unfolding of new ideas in physics is often tied to the development of combinatorial methods, and, conversely, problems in combinatorics have been successfully tackled using methods inspired by theoretical physics. We can thus speak nowadays of an emerging domain of Combinatorial Physics. The interference between these two disciplines is moreover an interference of multiple facets. Its best known manifestation (both to combinatorialists and theoretical physicists) has so far been the one between combinatorics and statistical physics, as statistical physics relies on an accurate counting of the various states or configurations of a physical system. But combinatorics and theoretical physics interact in various other ways. This book is mainly dedicated to the interactions of combinatorics (algebraic, enumerative, analytic) with (commutative and non-commutative) quantum field theory and tensor models, the latter being seen as a quantum field theoretical generalisation of matrix models.
Download or read book Combinatorial Physics written by Ted Bastin and published by World Scientific. This book was released on 1995 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors aim to reinstate a spirit of philosophical enquiry in physics. They abandon the intuitive continuum concepts and build up constructively a combinatorial mathematics of process. This radical change alone makes it possible to calculate the coupling constants of the fundamental fields which OCo via high energy scattering OCo are the bridge from the combinatorial world into dynamics. The untenable distinction between what is OCyobservedOCO, or measured, and what is not, upon which current quantum theory is based, is not needed. If we are to speak of mind, this has to be present OCo albeit in primitive form OCo at the most basic level, and not to be dragged in at one arbitrary point to avoid the difficulties about quantum observation. There is a growing literature on information-theoretic models for physics, but hitherto the two disciplines have gone in parallel. In this book they interact vitally."
Download or read book Combinatorics and Physics written by Kurusch Ebrahimi-Fard and published by American Mathematical Soc.. This book was released on 2011 with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is based on the mini-workshop Renormalization, held in December 2006, and the conference Combinatorics and Physics, held in March 2007. Both meetings took place at the Max-Planck-Institut fur Mathematik in Bonn, Germany. Research papers in the volume provide an overview of applications of combinatorics to various problems, such as applications to Hopf algebras, techniques to renormalization problems in quantum field theory, as well as combinatorial problems appearing in the context of the numerical integration of dynamical systems, in noncommutative geometry and in quantum gravity. In addition, it contains several introductory notes on renormalization Hopf algebras, Wilsonian renormalization and motives.
Download or read book Asymptotic Combinatorics with Application to Mathematical Physics written by V.A. Malyshev and published by Springer Science & Business Media. This book was released on 2002-08-31 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: New and striking results obtained in recent years from an intensive study of asymptotic combinatorics have led to a new, higher level of understanding of related problems: the theory of integrable systems, the Riemann-Hilbert problem, asymptotic representation theory, spectra of random matrices, combinatorics of Young diagrams and permutations, and even some aspects of quantum field theory.
Download or read book Combinatorics for Computer Science written by Stanley Gill Williamson and published by Courier Corporation. This book was released on 2002-01-01 with total page 548 pages. Available in PDF, EPUB and Kindle. Book excerpt: Useful guide covers two major subdivisions of combinatorics — enumeration and graph theory — with emphasis on conceptual needs of computer science. Each part is divided into a "basic concepts" chapter emphasizing intuitive needs of the subject, followed by four "topics" chapters that explore these ideas in depth. Invaluable practical resource for graduate students, advanced undergraduates, and professionals with an interest in algorithm design and other aspects of computer science and combinatorics. References for Linear Order & for Graphs, Trees, and Recursions. 219 figures.
Download or read book Physics and Combinatorics 2000 written by Anatol N. Kirillov and published by World Scientific. This book was released on 2001 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Nagoya 2000 International Workshop gathered together a group of scientists actively working in combinatorics, representation theory, special functions, number theory and mathematical physics, to acquaint the participants with some basic results in their fields and to discuss existing and possible interactions between the mentioned subjects. This volume constitutes the proceedings of the workshop. Contents: Vanishing Theorems and Character Formulas for the Hilbert Scheme of Points in the Plane (M Haiman); Exclusion Statistics and Chiral Partition Function (K Hikami); On the Spectrum of Dehn Twists in Quantum Teichmller Theory (R Kashaev); Introduction to Tropical Combinatorics (A Kirillov); Transition on Grothendieck Polynomials (A Lascoux); Generalized HAlder''s Theorem for Multiple Gamma Function (M Nishizawa); Quantum Calogero-Moser Models: Complete Integrability for All the Root Systems (R Sasaki); Simplification of Thermodynamic BetheOCoAnsatz Equations (M Takahashi); and other papers. Readership: Researchers and graduates in mathematical physics and combinatorics & graph theory."
Download or read book Asymptotic Combinatorics with Application to Mathematical Physics written by V.A. Malyshev and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 335 pages. Available in PDF, EPUB and Kindle. Book excerpt: New and striking results obtained in recent years from an intensive study of asymptotic combinatorics have led to a new, higher level of understanding of related problems: the theory of integrable systems, the Riemann-Hilbert problem, asymptotic representation theory, spectra of random matrices, combinatorics of Young diagrams and permutations, and even some aspects of quantum field theory.
Download or read book A Combinatorial Perspective on Quantum Field Theory written by Karen Yeats and published by Springer. This book was released on 2016-11-23 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explores combinatorial problems and insights in quantum field theory. It is not comprehensive, but rather takes a tour, shaped by the author’s biases, through some of the important ways that a combinatorial perspective can be brought to bear on quantum field theory. Among the outcomes are both physical insights and interesting mathematics. The book begins by thinking of perturbative expansions as kinds of generating functions and then introduces renormalization Hopf algebras. The remainder is broken into two parts. The first part looks at Dyson-Schwinger equations, stepping gradually from the purely combinatorial to the more physical. The second part looks at Feynman graphs and their periods. The flavour of the book will appeal to mathematicians with a combinatorics background as well as mathematical physicists and other mathematicians.
Download or read book Algebraic Combinatorics written by Chris Godsil and published by Routledge. This book was released on 2017-10-19 with total page 382 pages. Available in PDF, EPUB and Kindle. Book excerpt: This graduate level text is distinguished both by the range of topics and the novelty of the material it treats--more than half of the material in it has previously only appeared in research papers. The first half of this book introduces the characteristic and matchings polynomials of a graph. It is instructive to consider these polynomials together because they have a number of properties in common. The matchings polynomial has links with a number of problems in combinatorial enumeration, particularly some of the current work on the combinatorics of orthogonal polynomials. This connection is discussed at some length, and is also in part the stimulus for the inclusion of chapters on orthogonal polynomials and formal power series. Many of the properties of orthogonal polynomials are derived from properties of characteristic polynomials. The second half of the book introduces the theory of polynomial spaces, which provide easy access to a number of important results in design theory, coding theory and the theory of association schemes. This book should be of interest to second year graduate text/reference in mathematics.
Download or read book Asymptotic Combinatorics with Applications to Mathematical Physics written by Anatoly M. Vershik and published by Springer. This book was released on 2003-07-03 with total page 245 pages. Available in PDF, EPUB and Kindle. Book excerpt: At the Summer School Saint Petersburg 2001, the main lecture courses bore on recent progress in asymptotic representation theory: those written up for this volume deal with the theory of representations of infinite symmetric groups, and groups of infinite matrices over finite fields; Riemann-Hilbert problem techniques applied to the study of spectra of random matrices and asymptotics of Young diagrams with Plancherel measure; the corresponding central limit theorems; the combinatorics of modular curves and random trees with application to QFT; free probability and random matrices, and Hecke algebras.
Download or read book Q series written by George E. Andrews and published by American Mathematical Soc.. This book was released on 1986-01-01 with total page 146 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Introduction to Combinatorics written by A. B. Slomson and published by CRC Press. This book was released on 1997-02-01 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: The growth in digital devices, which require discrete formulation of problems, has revitalized the role of combinatorics, making it indispensable to computer science. Furthermore, the challenges of new technologies have led to its use in industrial processes, communications systems, electrical networks, organic chemical identification, coding theory, economics, and more. With a unique approach, Introduction to Combinatorics builds a foundation for problem-solving in any of these fields. Although combinatorics deals with finite collections of discrete objects, and as such differs from continuous mathematics, the two areas do interact. The author, therefore, does not hesitate to use methods drawn from continuous mathematics, and in fact shows readers the relevance of abstract, pure mathematics to real-world problems. The author has structured his chapters around concrete problems, and as he illustrates the solutions, the underlying theory emerges. His focus is on counting problems, beginning with the very straightforward and ending with the complicated problem of counting the number of different graphs with a given number of vertices. Its clear, accessible style and detailed solutions to many of the exercises, from routine to challenging, provided at the end of the book make Introduction to Combinatorics ideal for self-study as well as for structured coursework.
Download or read book q Series with Applications to Combinatorics Number Theory and Physics written by Bruce C. Berndt and published by American Mathematical Soc.. This book was released on 2001 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: The subject of $q$-series can be said to begin with Euler and his pentagonal number theorem. In fact, $q$-series are sometimes called Eulerian series. Contributions were made by Gauss, Jacobi, and Cauchy, but the first attempt at a systematic development, especially from the point of view of studying series with the products in the summands, was made by E. Heine in 1847. In the latter part of the nineteenth and in the early part of the twentieth centuries, two Englishmathematicians, L. J. Rogers and F. H. Jackson, made fundamental contributions. In 1940, G. H. Hardy described what we now call Ramanujan's famous $ 1\psi 1$ summation theorem as ``a remarkable formula with many parameters.'' This is now one of the fundamental theorems of the subject. Despite humble beginnings,the subject of $q$-series has flourished in the past three decades, particularly with its applications to combinatorics, number theory, and physics. During the year 2000, the University of Illinois embraced The Millennial Year in Number Theory. One of the events that year was the conference $q$-Series with Applications to Combinatorics, Number Theory, and Physics. This event gathered mathematicians from the world over to lecture and discuss their research. This volume presents nineteen of thepapers presented at the conference. The excellent lectures that are included chart pathways into the future and survey the numerous applications of $q$-series to combinatorics, number theory, and physics.
Download or read book Physics and Theoretical Computer Science written by Jean-Pierre Gazeau and published by IOS Press. This book was released on 2007 with total page 349 pages. Available in PDF, EPUB and Kindle. Book excerpt: Aims to reinforce the interface between physical sciences, theoretical computer science, and discrete mathematics. This book assembles theoretical physicists and specialists of theoretical informatics and discrete mathematics in order to learn about developments in cryptography, algorithmics, and more.
Download or read book Discrete Mathematics in Statistical Physics written by Martin Loebl and published by Springer Science & Business Media. This book was released on 2010-02-16 with total page 187 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book first describes connections between some basic problems and technics of combinatorics and statistical physics. The discrete mathematics and physics terminology are related to each other. Using the established connections, some exciting activities in one field are shown from a perspective of the other field. The purpose of the book is to emphasize these interactions as a strong and successful tool. In fact, this attitude has been a strong trend in both research communities recently. It also naturally leads to many open problems, some of which seem to be basic. Hopefully, this book will help making these exciting problems attractive to advanced students and researchers.
Download or read book Unitary Symmetry and Combinatorics written by James D. Louck and published by World Scientific. This book was released on 2008 with total page 642 pages. Available in PDF, EPUB and Kindle. Book excerpt: Notation -- Quantum angular momentum -- Composite systems -- Graphs and adjacency diagrams -- Generating functions -- The D[lambda] polynomials: form -- Operator actions in Hilbert space -- The D[lambda] polynomials: structure -- The general linear and unitary groups -- Tensor operator theory -- Compendium A. Basic algebraic objects -- Compendium B. Combinatorial objects.
