Seiberg-witten Theory And The Integrable Systems - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Seiberg-witten Theory And The Integrable Systems write by Andrei Marshakov. This book was released on 1999-03-26. Seiberg-witten Theory And The Integrable Systems available in PDF, EPUB and Kindle. In the past few decades many attempts have been made to search for a consistent formulation of quantum field theory beyond perturbation theory. One of the most interesting examples is the Seiberg-Witten ansatz for the N=2 SUSY supersymmetric Yang-Mills gauge theories in four dimensions. The aim of this book is to present in a clear form the main ideas of the relation between the exact solutions to the supersymmetric (SUSY) Yang-Mills theories and integrable systems. This relation is a beautiful example of reformulation of close-to-realistic physical theory in terms widely known in mathematical physics — systems of integrable nonlinear differential equations and their algebro-geometric solutions.First, the book reviews what is known about the physical problem: the construction of low-energy effective actions for the N=2 Yang-Mills theories from the traditional viewpoint of quantum field theory. Then the necessary background information from the theory of integrable systems is presented. In particular the author considers the definition of the algebro-geometric solutions to integrable systems in terms of complex curves or Riemann surfaces and the generating meromorphic 1-form. These definitions are illustrated in detail on the basic example of the periodic Toda chain.Several “toy-model” examples of string theory solutions where the structures of integrable systems appear are briefly discussed. Then the author proceeds to the Seiberg-Witten solutions and show that they are indeed defined by the same data as finite-gap solutions to integrable systems. The complete formulation requires the introduction of certain deformations of the finite-gap solutions described in terms of quasiclassical or Whitham hierarchies. The explicit differential equations and direct computations of the prepotential of the effective theory are presented and compared when possible with the well-known computations from supersymmetric quantum gauge theories.Finally, the book discusses the properties of the exact solutions to SUSY Yang-Mills theories and their relation to integrable systems in the general context of the modern approach to nonperturbative string or M-theory.
Seiberg-Witten Theory and Integrable Systems
Seiberg-Witten Theory and Integrable Systems - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Seiberg-Witten Theory and Integrable Systems write by Andrei Marshakov. This book was released on 1999. Seiberg-Witten Theory and Integrable Systems available in PDF, EPUB and Kindle. In the past few decades many attempts have been made to search for a consistent formulation of quantum field theory beyond perturbation theory. One of the most interesting examples is the Seiberg-Witten ansatz for the N=2 SUSY supersymmetric Yang-Mills gauge theories in four dimensions. The aim of this book is to present in a clear form the main ideas of the relation between the exact solutions to the supersymmetric (SUSY) Yang-Mills theories and integrable systems. This relation is a beautiful example of reformulation of close-to-realistic physical theory in terms widely known in mathematical physics ? systems of integrable nonlinear differential equations and their algebro-geometric solutions.First, the book reviews what is known about the physical problem: the construction of low-energy effective actions for the N=2 Yang-Mills theories from the traditional viewpoint of quantum field theory. Then the necessary background information from the theory of integrable systems is presented. In particular the author considers the definition of the algebro-geometric solutions to integrable systems in terms of complex curves or Riemann surfaces and the generating meromorphic 1-form. These definitions are illustrated in detail on the basic example of the periodic Toda chain.Several ?toy-model? examples of string theory solutions where the structures of integrable systems appear are briefly discussed. Then the author proceeds to the Seiberg-Witten solutions and show that they are indeed defined by the same data as finite-gap solutions to integrable systems. The complete formulation requires the introduction of certain deformations of the finite-gap solutions described in terms of quasiclassical or Whitham hierarchies. The explicit differential equations and direct computations of the prepotential of the effective theory are presented and compared when possible with the well-known computations from supersymmetric quantum gauge theories.Finally, the book discusses the properties of the exact solutions to SUSY Yang-Mills theories and their relation to integrable systems in the general context of the modern approach to nonperturbative string or M-theory.
Integrable Hierarchies and Modern Physical Theories
Integrable Hierarchies and Modern Physical Theories - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Integrable Hierarchies and Modern Physical Theories write by Henrik Aratyn. This book was released on 2012-12-06. Integrable Hierarchies and Modern Physical Theories available in PDF, EPUB and Kindle. Proceedings of the NATO Advanced Research Workshop, Chicago, USA, July 22-26, 2000
Application of Integrable Systems to Phase Transitions
Application of Integrable Systems to Phase Transitions - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Application of Integrable Systems to Phase Transitions write by C.B. Wang. This book was released on 2013-07-20. Application of Integrable Systems to Phase Transitions available in PDF, EPUB and Kindle. The eigenvalue densities in various matrix models in quantum chromodynamics (QCD) are ultimately unified in this book by a unified model derived from the integrable systems. Many new density models and free energy functions are consequently solved and presented. The phase transition models including critical phenomena with fractional power-law for the discontinuities of the free energies in the matrix models are systematically classified by means of a clear and rigorous mathematical demonstration. The methods here will stimulate new research directions such as the important Seiberg-Witten differential in Seiberg-Witten theory for solving the mass gap problem in quantum Yang-Mills theory. The formulations and results will benefit researchers and students in the fields of phase transitions, integrable systems, matrix models and Seiberg-Witten theory.
Notes on Seiberg-Witten Theory
Notes on Seiberg-Witten Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Notes on Seiberg-Witten Theory write by Liviu I. Nicolaescu. This book was released on 2000. Notes on Seiberg-Witten Theory available in PDF, EPUB and Kindle. After background on elliptic equations, Clifford algebras, Dirac operators, and Fredholm theory, chapters introduce solutions of the Seiberg-Witten equations and the group of gauge transformations, then look at algebraic surfaces. A final chapter presents in great detail a cut-and-paste technique for computing Seiberg-Witten invariants, covering elliptic equations on manifolds with cylindrical ends, finite energy monopoles on cylindrical manifolds, local and global properties of the moduli spaces of finite energy monopoles, and the process of reconstructing the space of monopoles on a 4-manifold decomposed into several parts by a hypersurface. Annotation copyrighted by Book News, Inc., Portland, OR.
