Download or read book Quantization and Infinite Dimensional Systems written by S.T. Ali and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 273 pages. Available in PDF, EPUB and Kindle. Book excerpt: As all participants know by now, the Bialowieza Summer Workshop has acquired a life of its own. The charming venue of the meetings, the informal atmosphere, the enthusiasm of the participants and the intensity of the scientific interaction have all conspired to make these meetings wonderful learning experiences. The XIIth Workshop (held from July 1 - 7, 1993) was once again a topical meeting within the general area of Differential Geometric Methods in Physics, focusing specifically on Quantization and Infinite-dimensional Systems. Altogether, about fifty participants attended the workshop. As before, the aim of the workshop was to have a small number of in-depth lectures on the main theme and a somewhat larger number of short presentations on related areas, while leaving enough free time for private discussions and exchange of ideas. Topics treated in the workshop included field theory, geometric quantization and symplectic geometry, coherent states methods, holomorphic representation theory, Poisson structures, non-commutative geometry, supersymmetry and quantum groups. The editors have the pleasant task of first thanking all the local organizers, in particular Dr. K. Gilewicz, for their painstaking efforts in ensuring the smooth running of the meeting and for organizing a delightful array of social events. Secondly, they would like to record their indebtedness to all the people who have contributed to this volume and to the redoubtable Ms. Cindy Parkinson without whose patient typesetting and editing skills the volume could hardly have seen the light of the day.
Download or read book Quantization Coherent States and Complex Structures written by J-P Antoine and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 289 pages. Available in PDF, EPUB and Kindle. Book excerpt: The XIIIth Bialowieza Summer Workshop was held from July 9 to 15, 1994. While still within the general framework of Differential Geometric Methods in Physics, the XnIth Workshop was expanded in scope to include quantum groups, q-deformations and non-commutative geometry. It is expected that lectures on these topics will now become an integral part of future workshops. In the more traditional areas, lectures were devoted to topics in quantization, field theory, group representations, coherent states, complex and Poisson structures, the Berry phase, graded contractions and some infinite-dimensional systems. Those of us who have taken part in the evolution of the workshops over the years, feel a good measure of satisfaction with the excellent quality of the papers presented, in particular the mathematical rigour and novelty. Each year a significant number of new results are presented and future directions of research are discussed. Their freshness and immediacy inevitably leads to intense discussions and an exchange of ideas in an informal and physically charming environment. The present workshop also had a higher attendance than its predecessors, with ap proximately 65 registered participants. As usual, there was a large number of graduate students and young researchers among them.
Download or read book Quantization of Fields with Infinite dimensional Invariance Groups Iii Generalized Schwinger feynman Theory written by BRYCE S. DEWITT and published by . This book was released on 1962 with total page 1 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinear field theories having elementary vertex functions of arbitrarily high order are presented. Emphasis is given to purely formal aspects of the theory which may be expected to survive generalization to situations in which standard asymptotic conditions are inapplicable. Since the context in which the field nonlinearities are assumed to appear is that of a non-Abelian infinite dimensional invariance group, detailed attention is given to the question of a group invariant measure for the Feynman functional integral. It is shown that the physically important part of the measure is not determined by the group. The theory of the propagators and correlation functions are also given which characterize the system when invariant variables are introduced. The existence of a c-number action functional which contains a complete description of all quantum processes is proved. The second variational derivatives of this functional constitute the wave operator for the one-particle propagators (including all radiative corrections) and its higher derivatives are the renormalized vertex functions. Finally, the implications for application to quantum gravidynamics are discussed. Because it leads to nonlocal covariant equations for a complex metric tensor the way is open to transmutations of topology at the quantum level. (Author).
Download or read book Stochastic and Infinite Dimensional Analysis written by Christopher C. Bernido and published by Birkhäuser. This book was released on 2016-08-10 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents a collection of papers covering applications from a wide range of systems with infinitely many degrees of freedom studied using techniques from stochastic and infinite dimensional analysis, e.g. Feynman path integrals, the statistical mechanics of polymer chains, complex networks, and quantum field theory. Systems of infinitely many degrees of freedom create their particular mathematical challenges which have been addressed by different mathematical theories, namely in the theories of stochastic processes, Malliavin calculus, and especially white noise analysis. These proceedings are inspired by a conference held on the occasion of Prof. Ludwig Streit’s 75th birthday and celebrate his pioneering and ongoing work in these fields.
Download or read book Quantization of Fields with Infinite dimensional Invariance Groups Ii Anticommuting Fields written by BRYCE S. DEWITT and published by . This book was released on 1961 with total page 1 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Green's function approach to the definition of commutators for fields possessing infinite dimensional invariance groups is extended to the case of anticommuting fields. The discussion is restricted to fields which provide linear homogeneous or inhomogeneous representations of the group, a restriction which excludes no case of practical interest and facilitates setting up the formalism in a manifestly covariant way. Selfconsistency of supplementary conditions, Huygens' principle and reciprocity relations are established just as for commuting fields. Careful attention must be paid to the ordering of anticommuting factors, particularly in the demonstration of the Poisson-Jacobi identity. The invariance properties of the Poisson bracket are investigated in detail and the notion of conditional invariant is introduced. A special class of conditional invariants called asymptotic invariants, which give a complete physical characterization of initial and final states of the dynamical system, is studied. (Author).
Download or read book Spectral Methods in Infinite Dimensional Analysis written by Yu.M. Berezansky and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 983 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Russian edition of this book appeared 5 years ago. Since that time, many results have been improved upon and new approaches to the problems investigated in the book have appeared. But the greatest surprise for us was to discover that there exists a large group of mathematicians working in the area of the so-called White Noise Analysis which is closely connected with the essential part of our book, namely, with the theory of generalized functions of infinitely many variables. The first papers dealing with White Noise Analysis were written by T. Hida in Japan in 1975. Later, this analysis was devel oped intensively in Japan, Germany, U.S.A., Taipei, and in other places. The related problems of infinite-dimensional analysis have been studied in Kiev since 1967, and the theory of generalized functions of infinitely many variables has been in vestigated since 1973. However, due to the political system in the U.S.S.R., contact be tween Ukrainian and foreign mathematicians was impossible for a long period of time. This is why, to our great regret, only at the end of 1988 did one of the authors meet L. Streit who told him about the existence of White Noise Analysis. And it become clear that many results in these two theories coincide and that, in fact, there exists a single theory and not two distinct ones.
Download or read book Some Formulae with Logarithmic Derivatives Related to a Quantization of Some Infinite dimensional Hamiltonian Systems written by O. G. Smolyanov and published by . This book was released on 1996 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Quantization And Coherent States Methods Proceedings Of Xi Workshop On Geometric Methods In Physics written by S Twareque Ali and published by World Scientific. This book was released on 1993-10-29 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of the conference was to find common elements between quantization and coherent states, and quantization on Poisson manifolds. Topics included are coherent states, geometric quantization, phase space quantization, deformation and *-products and Berry's phase.
Download or read book Probability Theory and Mathematical Statistics Vol 2 written by B. Grigelionis and published by Walter de Gruyter GmbH & Co KG. This book was released on 2020-05-18 with total page 624 pages. Available in PDF, EPUB and Kindle. Book excerpt: No detailed description available for "PROB. TH. MATH. ST. ( GRIGELIONIS) VOL. 2 PROC.5/1989 E-BOOK".
Download or read book Quantization of Fields with Infinite dimensional Invariance Groups written by Bryce Seligman DeWitt and published by . This book was released on 1960 with total page 70 pages. Available in PDF, EPUB and Kindle. Book excerpt: A general approach to the problems of quantizing fields which have infinite dimensional invariance groups is given. Space and time are treated on a completely equal footing. A Poisson bracket is defined by means of Green's functions, independently of the discovery or recognition of canonical variables, and is shown to satisfy all the usual identities. In accordance with the measurement theoretical foundations of the quantum theorgy, the Poisson bracket (i.e., commutator) is defined only for physically measurable group invariants. The Green's functions give a direct description of the propagation of small disturbances arising from a pair of mutally interfering measurements.
Download or read book Infinite Dimensional Systems written by Franz Kappel and published by . This book was released on 2014-01-15 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Mathematical Foundations of Quantum Mechanics written by George W. Mackey and published by Courier Corporation. This book was released on 2013-12-31 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt: This graduate-level text introduces fundamentals of classical mechanics; surveys basics of quantum mechanics; and concludes with a look at group theory and quantum mechanics of the atom. 1963 edition.
Download or read book Exact Treatment of Finite dimensional and Infinite dimensional Quantum Systems written by Tomislav Predavač Živković and published by . This book was released on 2010 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: There are very few quantum systems that can be solved exactly. In most cases, one has to use some approximate method. One of the most important approximate methods is perturbation expansion. The main idea of this method is simple: if one knows the solution of some parent system, one can find the solution of the "perturbed" system. It is assumed that the system does not differ from the parent system very much, in which case "perturbation" is small. Next one expresses eigenvalues and eigenstates of the perturbed systems as a power series expansion in terms of the eigenvalues and eigenstates of the parent system. Hence in order to obtain the solution of the perturbed system, one has to know the solution of the parent system. This book offers examples and solutions to this fascinating topic.
Download or read book Heat Kernels and Analysis on Manifolds Graphs and Metric Spaces written by Pascal Auscher and published by American Mathematical Soc.. This book was released on 2003 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the expanded lecture notes of courses taught at the Emile Borel Centre of the Henri Poincare Institute (Paris). In the book, leading experts introduce recent research in their fields. The unifying theme is the study of heat kernels in various situations using related geometric and analytic tools. Topics include analysis of complex-coefficient elliptic operators, diffusions on fractals and on infinite-dimensional groups, heat kernel and isoperimetry on Riemannian manifolds, heat kernels and infinite dimensional analysis, diffusions and Sobolev-type spaces on metric spaces, quasi-regular mappings and $p$-Laplace operators, heat kernel and spherical inversion on $SL 2(C)$, random walks and spectral geometry on crystal lattices, isoperimetric and isocapacitary inequalities, and generating function techniques for random walks on graphs. This volume is suitable for graduate students and research mathematicians interested in random processes and analysis on manifolds.
Download or read book Quantum Theory Groups and Representations written by Peter Woit and published by Springer. This book was released on 2017-11-01 with total page 659 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text systematically presents the basics of quantum mechanics, emphasizing the role of Lie groups, Lie algebras, and their unitary representations. The mathematical structure of the subject is brought to the fore, intentionally avoiding significant overlap with material from standard physics courses in quantum mechanics and quantum field theory. The level of presentation is attractive to mathematics students looking to learn about both quantum mechanics and representation theory, while also appealing to physics students who would like to know more about the mathematics underlying the subject. This text showcases the numerous differences between typical mathematical and physical treatments of the subject. The latter portions of the book focus on central mathematical objects that occur in the Standard Model of particle physics, underlining the deep and intimate connections between mathematics and the physical world. While an elementary physics course of some kind would be helpful to the reader, no specific background in physics is assumed, making this book accessible to students with a grounding in multivariable calculus and linear algebra. Many exercises are provided to develop the reader's understanding of and facility in quantum-theoretical concepts and calculations.
Download or read book What Is a Quantum Field Theory written by Michel Talagrand and published by Cambridge University Press. This book was released on 2022-03-17 with total page 759 pages. Available in PDF, EPUB and Kindle. Book excerpt: A lively and erudite introduction for readers with a background in undergraduate mathematics but no previous knowledge of physics.
Download or read book Introduction to the Statistical Physics of Integrable Many body Systems written by Ladislav Šamaj and published by Cambridge University Press. This book was released on 2013-05-16 with total page 525 pages. Available in PDF, EPUB and Kindle. Book excerpt: Including topics not traditionally covered in literature, such as (1+1)-dimensional QFT and classical 2D Coulomb gases, this book considers a wide range of models and demonstrates a number of situations to which they can be applied. Beginning with a treatise of nonrelativistic 1D continuum Fermi and Bose quantum gases of identical spinless particles, the book describes the quantum inverse scattering method and the analysis of the related Yang–Baxter equation and integrable quantum Heisenberg models. It also discusses systems within condensed matter physics, the complete solution of the sine-Gordon model and modern trends in the thermodynamic Bethe ansatz. Each chapter concludes with problems and solutions to help consolidate the reader's understanding of the theory and its applications. Basic knowledge of quantum mechanics and equilibrium statistical physics is assumed, making this book suitable for graduate students and researchers in statistical physics, quantum mechanics and mathematical and theoretical physics.
