Physical Combinatorics
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Author | : Masaki Kashiwara |
Publisher | : Springer Science & Business Media |
Total Pages | : 321 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1461213789 |
Taking into account the various criss-crossing among mathematical subject, Physical Combinatorics presents new results and exciting ideas from three viewpoints; representation theory, integrable models, and combinatorics. This work is concerned with combinatorial aspects arising in the theory of exactly solvable models and representation theory. Recent developments in integrable models reveal an unexpected link between representation theory and statistical mechanics through combinatorics.
Author | : Adrian Tanasa |
Publisher | : Oxford University Press |
Total Pages | : 409 |
Release | : 2021 |
Genre | : Computers |
ISBN | : 0192895494 |
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.
Author | : Kurusch Ebrahimi-Fard |
Publisher | : American Mathematical Soc. |
Total Pages | : 480 |
Release | : 2011 |
Genre | : Mathematics |
ISBN | : 0821853295 |
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.
Author | : Adrian Tanasa |
Publisher | : Oxford University Press |
Total Pages | : 420 |
Release | : 2021-04-16 |
Genre | : Mathematics |
ISBN | : 0192648063 |
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.
Author | : Anatoly M. Vershik |
Publisher | : Springer |
Total Pages | : 245 |
Release | : 2003-07-03 |
Genre | : Mathematics |
ISBN | : 354044890X |
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.
Author | : V.A. Malyshev |
Publisher | : Springer Science & Business Media |
Total Pages | : 335 |
Release | : 2012-12-06 |
Genre | : Science |
ISBN | : 9401005753 |
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.
Author | : Ted Bastin |
Publisher | : World Scientific |
Total Pages | : 188 |
Release | : 1995 |
Genre | : Science |
ISBN | : 9812796142 |
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."
Author | : Ke. Ḍī Jhā |
Publisher | : Discovery Publishing House |
Total Pages | : 320 |
Release | : 2009 |
Genre | : Chemistry, Physical and theoretical |
ISBN | : 9788183564458 |
Author | : Philippe Flajolet |
Publisher | : Cambridge University Press |
Total Pages | : 825 |
Release | : 2009-01-15 |
Genre | : Mathematics |
ISBN | : 1139477161 |
Analytic combinatorics aims to enable precise quantitative predictions of the properties of large combinatorial structures. The theory has emerged over recent decades as essential both for the analysis of algorithms and for the study of scientific models in many disciplines, including probability theory, statistical physics, computational biology, and information theory. With a careful combination of symbolic enumeration methods and complex analysis, drawing heavily on generating functions, results of sweeping generality emerge that can be applied in particular to fundamental structures such as permutations, sequences, strings, walks, paths, trees, graphs and maps. This account is the definitive treatment of the topic. The authors give full coverage of the underlying mathematics and a thorough treatment of both classical and modern applications of the theory. The text is complemented with exercises, examples, appendices and notes to aid understanding. The book can be used for an advanced undergraduate or a graduate course, or for self-study.
Author | : Stanley Gill Williamson |
Publisher | : Courier Corporation |
Total Pages | : 548 |
Release | : 2002-01-01 |
Genre | : Mathematics |
ISBN | : 9780486420769 |
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.