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| 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 | : 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 | : 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 | : Karen Yeats |
| Publisher | : Springer |
| Total Pages | : 120 |
| Release | : 2016-11-23 |
| Genre | : Science |
| ISBN | : 3319475517 |
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.
| Author | : Alexander K. Hartmann |
| Publisher | : John Wiley & Sons |
| Total Pages | : 360 |
| Release | : 2006-05-12 |
| Genre | : Science |
| ISBN | : 3527606866 |
A concise, comprehensive introduction to the topic of statistical physics of combinatorial optimization, bringing together theoretical concepts and algorithms from computer science with analytical methods from physics. The result bridges the gap between statistical physics and combinatorial optimization, investigating problems taken from theoretical computing, such as the vertex-cover problem, with the concepts and methods of theoretical physics. The authors cover rapid developments and analytical methods that are both extremely complex and spread by word-of-mouth, providing all the necessary basics in required detail. Throughout, the algorithms are shown with examples and calculations, while the proofs are given in a way suitable for graduate students, post-docs, and researchers. Ideal for newcomers to this young, multidisciplinary field.
| 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 | : 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.
| 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 | : Dmitri Rabounski |
| Publisher | : Infinite Study |
| Total Pages | : 72 |
| Release | : |
| Genre | : |
| ISBN | : |
Progress in Physics has been created for publications on advanced studies in theoretical and experimental physics, including related themes from mathematics.
