Combinatorial Physics
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Combinatorial Physics
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Author : Ted Bastin
language : en
Publisher: World Scientific
Release Date : 1995
Combinatorial Physics written by Ted Bastin and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Science categories.
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."
Combinatorial Physics
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Author : Adrian Tanasa
language : en
Publisher: Oxford University Press
Release Date : 2021-04-16
Combinatorial Physics written by Adrian Tanasa and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-04-16 with Mathematics categories.
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.
A Combinatorial Perspective On Quantum Field Theory
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Author : Karen Yeats
language : en
Publisher: Springer
Release Date : 2016-11-23
A Combinatorial Perspective On Quantum Field Theory written by Karen Yeats and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-11-23 with Science categories.
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.
Quantum Fields And Processes
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Author : John Gough
language : en
Publisher: Cambridge University Press
Release Date : 2018-04-12
Quantum Fields And Processes written by John Gough and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-04-12 with Mathematics categories.
Do quantum field theory without Feynman diagrams! Use the combinatorics behind cumulants, correlations, Green's functions and quantum fields.
Combinatorics And Physics
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Author : Kurusch Ebrahimi-Fard
language : en
Publisher: American Mathematical Soc.
Release Date : 2011
Combinatorics And Physics written by Kurusch Ebrahimi-Fard and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Mathematics categories.
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.
Phase Transitions In Combinatorial Optimization Problems
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Author : Alexander K. Hartmann
language : en
Publisher: John Wiley & Sons
Release Date : 2006-05-12
Phase Transitions In Combinatorial Optimization Problems written by Alexander K. Hartmann and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-05-12 with Science categories.
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.
Colored Discrete Spaces
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Author : Luca Lionni
language : en
Publisher: Springer
Release Date : 2018-08-01
Colored Discrete Spaces written by Luca Lionni and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-08-01 with Science categories.
This book provides a number of combinatorial tools that allow a systematic study of very general discrete spaces involved in the context of discrete quantum gravity. In any dimension D, we can discretize Euclidean gravity in the absence of matter over random discrete spaces obtained by gluing families of polytopes together in all possible ways. These spaces are then classified according to their curvature. In D=2, it results in a theory of random discrete spheres, which converge in the continuum limit towards the Brownian sphere, a random fractal space interpreted as a quantum random space-time. In this limit, the continuous Liouville theory of D=2 quantum gravity is recovered. Previous results in higher dimension regarded triangulations, converging towards a continuum random tree, or gluings of simple building blocks of small sizes, for which multi-trace matrix model results are recovered in any even dimension. In this book, the author develops a bijection with stacked two-dimensional discrete surfaces for the most general colored building blocks, and details how it can be used to classify colored discrete spaces according to their curvature. The way in which this combinatorial problem arrises in discrete quantum gravity and random tensor models is discussed in detail.
Physical Combinatorics
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Author : Masaki Kashiwara
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Physical Combinatorics written by Masaki Kashiwara and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
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.
Combinatorial Aspects Of Scattering Amplitudes
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Author : Matteo Parisi
language : en
Publisher: Springer Nature
Release Date : 2023-12-11
Combinatorial Aspects Of Scattering Amplitudes written by Matteo Parisi and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-12-11 with Science categories.
This book is a significant contribution within and across High Energy Physics and Algebraic Combinatorics. It is at the forefront of the recent paradigm shift according to which physical observables emerge from geometry and combinatorics. It is the first book on the amplituhedron, which encodes the scattering amplitudes of N=4 Yang-Mills theory, a cousin of the theory of strong interactions of quarks and gluons. Amplituhedra are generalizations of polytopes inside the Grassmannian, and they build on the theory of total positivity and oriented matroids. This book unveils many new combinatorial structures of the amplituhedron and introduces a new important related object, the momentum amplituhedron. Moreover, the work pioneers the connection between amplituhedra, cluster algebras and tropical geometry. Combining extensive introductions with proofs and examples, it is a valuable resource for researchers investigating geometrical structures emerging from physics for some time to come.
Asymptotic Combinatorics With Application To Mathematical Physics
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Author : V.A. Malyshev
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Asymptotic Combinatorics With Application To Mathematical Physics written by V.A. Malyshev and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.
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.