The C And A Theorems And The Local Renormalisation Group
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The C And A Theorems And The Local Renormalisation Group
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Author : Graham Shore
language : en
Publisher: Springer
Release Date : 2017-03-30
The C And A Theorems And The Local Renormalisation Group written by Graham Shore and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-03-30 with Science categories.
The Zamolodchikov c-theorem has led to important new insights in the understanding of the Renormalisation Group (RG) and the geometry of the space of QFTs. The present primer introduces and reviews the parallel developments of the search for a higher-dimensional generalisation of the c-theorem and of the Local RG (LRG). The idea of renormalisation with position-dependent couplings, running under local Weyl scaling, is traced from its early realisations to the elegant modern formalism of the LRG. The key rôle of the associated Weyl consistency conditions in establishing RG flow equations for the coefficients of the trace anomaly in curved spacetime, and their relation to the c-theorem and four-dimensional a-theorem, is explained in detail. A number of different derivations of the c-theorem in two dimensions are presented and subsequently generalised to four dimensions. The obstructions to establishing monotonic C-functions related to the trace anomaly coefficients in four dimensions are explained. The possibility of deriving an a-theorem for the coefficient of the Euler-Gauss-Bonnet density is explored, initially by formulating the QFT on maximally symmetric spaces. Then the formulation of the weak a-theorem using a dispersion relation for four-point functions is presented. Finally, the application of the LRG to the issue of limit cycles in theories with a global symmetry is described, shedding new light on the geometry of the space of couplings in QFT.
The C And A Theorems And The Local Renormalisation Group
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Author : Graham Shore
language : en
Publisher:
Release Date : 2017
The C And A Theorems And The Local Renormalisation Group written by Graham Shore and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017 with Mathematical physics categories.
Birational Geometry K Hler Einstein Metrics And Degenerations
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Author : Ivan Cheltsov
language : en
Publisher: Springer Nature
Release Date : 2023-05-23
Birational Geometry K Hler Einstein Metrics And Degenerations written by Ivan Cheltsov and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-05-23 with Mathematics categories.
This book collects the proceedings of a series of conferences dedicated to birational geometry of Fano varieties held in Moscow, Shanghai and Pohang The conferences were focused on the following two related problems: • existence of Kähler–Einstein metrics on Fano varieties • degenerations of Fano varieties on which two famous conjectures were recently proved. The first is the famous Borisov–Alexeev–Borisov Conjecture on the boundedness of Fano varieties, proved by Caucher Birkar (for which he was awarded the Fields medal in 2018), and the second one is the (arguably even more famous) Tian–Yau–Donaldson Conjecture on the existence of Kähler–Einstein metrics on (smooth) Fano varieties and K-stability, which was proved by Xiuxiong Chen, Sir Simon Donaldson and Song Sun. The solutions for these longstanding conjectures have opened new directions in birational and Kähler geometries. These research directions generated new interesting mathematical problems, attracting the attention of mathematicians worldwide. These conferences brought together top researchers in both fields (birational geometry and complex geometry) to solve some of these problems and understand the relations between them. The result of this activity is collected in this book, which contains contributions by sixty nine mathematicians, who contributed forty three research and survey papers to this volume. Many of them were participants of the Moscow–Shanghai–Pohang conferences, while the others helped to expand the research breadth of the volume—the diversity of their contributions reflects the vitality of modern Algebraic Geometry.
Emergent Gauge Symmetries In Particle Physics And Cosmology
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Author : Steven D Bass
language : en
Publisher: World Scientific
Release Date : 2025-03-21
Emergent Gauge Symmetries In Particle Physics And Cosmology written by Steven D Bass and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-03-21 with Science categories.
The Standard Model and General Relativity provide an excellent description of our present measurements in particle physics and gravitation. Yet we know that new physics is needed. Puzzles include tiny neutrino masses, baryogenesis (the matter-antimatter asymmetry in the Universe), dark energy and dark matter as well as the physics associated with primordial inflation.The book develops the idea of an emergent Standard Model: that its gauge symmetries and particles might be 'born' in a topological like phase transition deep in the ultraviolet with the Standard Model parameters (the masses and couplings) linked to the stability of the vacuum. With emergence the gauge symmetries would 'dissolve' in the extreme ultraviolet instead of extra unification. Neutrinos would be their own antiparticles. The cosmological constant scale comes out naturally in this approach, similar in size to the value of light Majorana neutrino masses. There are also interesting constraints on dark matter scenarios. Following an introduction to the Standard Model and the present status of our knowledge of fundamental interactions, the book discusses the key ideas of vacuum stability and emergent gauge symmetries. The phenomenology of an emergent Standard Model and its consequences for cosmology and early Universe physics are then explored. With a new generation of experiments both in particle and gravitational physics soon to begin plus expected advances in cosmology, the book serves both as an introduction and invitation to join new thinking in this physics with possible deep connections between the world of experiments and physics in the far ultraviolet.
Renormalization Group 91 Proceedings Of The 2nd International Conference
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Author : Dmitri V Shirkov
language : en
Publisher: World Scientific
Release Date : 1992-04-30
Renormalization Group 91 Proceedings Of The 2nd International Conference written by Dmitri V Shirkov and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-04-30 with categories.
The papers included here deal with the many faces of renormalization group formalism as it is used in different branches of theoretical physics. The subjects covered emphasize various applications to the theory of turbulence, chaos, quantum chaos in dynamical systems, spin systems and vector models. Also discussed are applications to related topics such as quantum field theory and chromodynamics, high temperature superconductivity and plasma physics.
Renormalization And Effective Field Theory
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Author : Kevin Costello
language : en
Publisher: American Mathematical Society
Release Date : 2022-04-25
Renormalization And Effective Field Theory written by Kevin Costello and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-04-25 with Mathematics categories.
This book tells mathematicians about an amazing subject invented by physicists and it tells physicists how a master mathematician must proceed in order to understand it. Physicists who know quantum field theory can learn the powerful methodology of mathematical structure, while mathematicians can position themselves to use the magical ideas of quantum field theory in “mathematics” itself. The retelling of the tale mathematically by Kevin Costello is a beautiful tour de force. —Dennis Sullivan This book is quite a remarkable contribution. It should make perturbative quantum field theory accessible to mathematicians. There is a lot of insight in the way the author uses the renormalization group and effective field theory to analyze perturbative renormalization; this may serve as a springboard to a wider use of those topics, hopefully to an eventual nonperturbative understanding. —Edward Witten Quantum field theory has had a profound influence on mathematics, and on geometry in particular. However, the notorious difficulties of renormalization have made quantum field theory very inaccessible for mathematicians. This book provides complete mathematical foundations for the theory of perturbative quantum field theory, based on Wilson's ideas of low-energy effective field theory and on the Batalin–Vilkovisky formalism. As an example, a cohomological proof of perturbative renormalizability of Yang–Mills theory is presented. An effort has been made to make the book accessible to mathematicians who have had no prior exposure to quantum field theory. Graduate students who have taken classes in basic functional analysis and homological algebra should be able to read this book.
Nonlinear Dynamics And Renormalization Group
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Author : Israel Michael Sigal
language : en
Publisher: American Mathematical Soc.
Release Date : 2001
Nonlinear Dynamics And Renormalization Group written by Israel Michael Sigal 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 2001 with Mathematics categories.
This book contains the proceedings from the workshop, Nonlinear Dynamics and Renormalization Group, held at the Centre de recherches mathématiques (CRM) in Montréal (Canada), as part of the year-long program devoted to mathematical physics. In the book, active researchers in the fields of nonlinear partial differential equations and renormalization group contribute recent results on topics such as Ginzburg-Landau equations and blow-up of solutions of the nonlinear Schroedinger equations, quantum resonances, and renormalization group analysis in constructive quantum field theory. This volume offers the latest research in the rapidly developing fields of nonlinear equations and renormalization group.
Introduction To A Renormalisation Group Method
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Author : Roland Bauerschmidt
language : en
Publisher: Springer Nature
Release Date : 2019-10-16
Introduction To A Renormalisation Group Method written by Roland Bauerschmidt and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-10-16 with Science categories.
This is a primer on a mathematically rigorous renormalisation group theory, presenting mathematical techniques fundamental to renormalisation group analysis such as Gaussian integration, perturbative renormalisation and the stable manifold theorem. It also provides an overview of fundamental models in statistical mechanics with critical behaviour, including the Ising and φ4 models and the self-avoiding walk. The book begins with critical behaviour and its basic discussion in statistical mechanics models, and subsequently explores perturbative and non-perturbative analysis in the renormalisation group. Lastly it discusses the relation of these topics to the self-avoiding walk and supersymmetry. Including exercises in each chapter to help readers deepen their understanding, it is a valuable resource for mathematicians and mathematical physicists wanting to learn renormalisation group theory.
Holomorphic Dynamics And Renormalization
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Author : Mikhail Lyubich
language : en
Publisher: American Mathematical Soc.
Release Date : 2008
Holomorphic Dynamics And Renormalization written by Mikhail Lyubich 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 2008 with Mathematics categories.
Collects papers that reflect some of the directions of research in two closely related fields: Complex Dynamics and Renormalization in Dynamical Systems. This title contains papers that introduces the reader to this fascinating world and a related area of transcendental dynamics. It also includes open problems and computer simulations.
Confinement Duality And Nonperturbative Aspects Of Qcd
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Author : Pierre van Baal
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-12-11
Confinement Duality And Nonperturbative Aspects Of Qcd written by Pierre van Baal 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 2005-12-11 with Science categories.
Proceedings of a NATO ASI and Isaac Newton Institute Workshop held in Cambridge, UK, June 23-July 4, 1997