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Author: Adrian Tanasa
Publisher: Oxford University Press
ISBN: 0192895494
Category : Computers
Languages : en
Pages : 409
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Book Description
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: Adrian Tanasa
Publisher: Oxford University Press
ISBN: 0192895494
Category : Computers
Languages : en
Pages : 409
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Book Description
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: Louis H Kauffman
Publisher: World Scientific
ISBN: 9814500623
Category : Science
Languages : en
Pages : 188
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Book Description
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 — via high energy scattering — are the bridge from the combinatorial world into dynamics. The untenable distinction between what is ‘observed’, 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 — albeit in primitive form — 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: V.A. Malyshev
Publisher: Springer Science & Business Media
ISBN: 9781402007927
Category : Science
Languages : en
Pages : 352
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Book Description
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: Kurusch Ebrahimi-Fard
Publisher: American Mathematical Soc.
ISBN: 0821853295
Category : Mathematics
Languages : en
Pages : 480
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Book Description
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: Alexander K. Hartmann
Publisher: John Wiley & Sons
ISBN: 3527606866
Category : Science
Languages : en
Pages : 360
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Book Description
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: Richard A. Brualdi
Publisher: CRC Press
ISBN: 9781420082241
Category : Mathematics
Languages : en
Pages : 288
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Book Description
Unlike most elementary books on matrices, A Combinatorial Approach to Matrix Theory and Its Applications employs combinatorial and graph-theoretical tools to develop basic theorems of matrix theory, shedding new light on the subject by exploring the connections of these tools to matrices. After reviewing the basics of graph theory, elementary counting formulas, fields, and vector spaces, the book explains the algebra of matrices and uses the König digraph to carry out simple matrix operations. It then discusses matrix powers, provides a graph-theoretical definition of the determinant using the Coates digraph of a matrix, and presents a graph-theoretical interpretation of matrix inverses. The authors develop the elementary theory of solutions of systems of linear equations and show how to use the Coates digraph to solve a linear system. They also explore the eigenvalues, eigenvectors, and characteristic polynomial of a matrix; examine the important properties of nonnegative matrices that are part of the Perron–Frobenius theory; and study eigenvalue inclusion regions and sign-nonsingular matrices. The final chapter presents applications to electrical engineering, physics, and chemistry. Using combinatorial and graph-theoretical tools, this book enables a solid understanding of the fundamentals of matrix theory and its application to scientific areas.
Author: Karen Yeats
Publisher: Springer
ISBN: 3319475517
Category : Science
Languages : en
Pages : 120
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Book Description
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: R.L. Graham
Publisher: Elsevier
ISBN: 044488002X
Category : Business & Economics
Languages : en
Pages : 1283
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Book Description
Author: V.A. Malyshev
Publisher: Springer Science & Business Media
ISBN: 9401005753
Category : Science
Languages : en
Pages : 335
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Book Description
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: Marc Mézard
Publisher: Oxford University Press
ISBN: 019857083X
Category : Computers
Languages : en
Pages : 584
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Book Description
A very active field of research is emerging at the frontier of statistical physics, theoretical computer science/discrete mathematics, and coding/information theory. This book sets up a common language and pool of concepts, accessible to students and researchers from each of these fields.
