Path Integrals On Manifolds With Boundary And Their Asymptotic Expansions

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Space – Time – Matter

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Author : Jochen Brüning
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110452154
Total Pages : 518 pages
Book Rating : 4.1/5 (14 download)

Book Synopsis Space – Time – Matter by : Jochen Brüning

Download or read book Space – Time – Matter written by Jochen Brüning and published by Walter de Gruyter GmbH & Co KG. This book was released on 2018-04-09 with total page 518 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph describes some of the most interesting results obtained by the mathematicians and physicists collaborating in the CRC 647 "Space – Time – Matter", in the years 2005 - 2016. The work presented concerns the mathematical and physical foundations of string and quantum field theory as well as cosmology. Important topics are the spaces and metrics modelling the geometry of matter, and the evolution of these geometries. The partial differential equations governing such structures and their singularities, special solutions and stability properties are discussed in detail. Contents Introduction Algebraic K-theory, assembly maps, controlled algebra, and trace methods Lorentzian manifolds with special holonomy – Constructions and global properties Contributions to the spectral geometry of locally homogeneous spaces On conformally covariant differential operators and spectral theory of the holographic Laplacian Moduli and deformations Vector bundles in algebraic geometry and mathematical physics Dyson–Schwinger equations: Fix-point equations for quantum fields Hidden structure in the form factors ofN = 4 SYM On regulating the AdS superstring Constraints on CFT observables from the bootstrap program Simplifying amplitudes in Maxwell-Einstein and Yang-Mills-Einstein supergravities Yangian symmetry in maximally supersymmetric Yang-Mills theory Wave and Dirac equations on manifolds Geometric analysis on singular spaces Singularities and long-time behavior in nonlinear evolution equations and general relativity

Euclidean Quantum Gravity on Manifolds with Boundary

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Author : Giampiero Esposito
Publisher : Springer Science & Business Media
ISBN 13 : 9401158061
Total Pages : 334 pages
Book Rating : 4.4/5 (11 download)

Book Synopsis Euclidean Quantum Gravity on Manifolds with Boundary by : Giampiero Esposito

Download or read book Euclidean Quantum Gravity on Manifolds with Boundary written by Giampiero Esposito and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 334 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book reflects our own struggle to understand the semiclassical behaviour of quantized fields in the presence of boundaries. Along many years, motivated by the problems of quantum cosmology and quantum field theory, we have studied in detail the one-loop properties of massless spin-l/2 fields, Euclidean Maxwell the ory, gravitino potentials and Euclidean quantum gravity. Hence our book begins with a review of the physical and mathematical motivations for studying physical theories in the presence of boundaries, with emphasis on electrostatics, vacuum v Maxwell theory and quantum cosmology. We then study the Feynman propagator in Minkowski space-time and in curved space-time. In the latter case, the corre sponding Schwinger-DeWitt asymptotic expansion is given. The following chapters are devoted to the standard theory of the effective action and the geometric im provement due to Vilkovisky, the manifestly covariant quantization of gauge fields, zeta-function regularization in mathematics and in quantum field theory, and the problem of boundary conditions in one-loop quantum theory. For this purpose, we study in detail Dirichlet, Neumann and Robin boundary conditions for scalar fields, local and non-local boundary conditions for massless spin-l/2 fields, mixed boundary conditions for gauge fields and gravitation. This is the content of Part I. Part II presents our investigations of Euclidean Maxwell theory, simple super gravity and Euclidean quantum gravity.

Spectral Geometry of Manifolds with Boundary and Decomposition of Manifolds

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Author : Gerd Grubb
Publisher : American Mathematical Soc.
ISBN 13 : 082183536X
Total Pages : 338 pages
Book Rating : 4.8/5 (218 download)

Book Synopsis Spectral Geometry of Manifolds with Boundary and Decomposition of Manifolds by : Gerd Grubb

Download or read book Spectral Geometry of Manifolds with Boundary and Decomposition of Manifolds written by Gerd Grubb and published by American Mathematical Soc.. This book was released on 2005 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years, increasingly complex methods have been brought into play in the treatment of geometric and topological problems for partial differential operators on manifolds. This collection of papers, resulting from a Workshop on Spectral Geometry of Manifolds with Boundary and Decomposition of Manifolds, provides a broad picture of these methods with new results. Subjects in the book cover a wide variety of topics, from recent advances in index theory and the more general boundary, to applications of those invariants in geometry, topology, and physics. Papers are grouped into four parts: Part I gives an overview of the subject from various points of view. Part II deals with spectral invariants, such as geometric and topological questions. Part IV deals specifically with problems on manifolds with singularities. The book is suitable for graduate students and researchers interested in spectral problems in geometry.

Aspects of Boundary Problems in Analysis and Geometry

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Author : Juan Gil
Publisher : Birkhäuser
ISBN 13 : 3034878508
Total Pages : 574 pages
Book Rating : 4.0/5 (348 download)

Book Synopsis Aspects of Boundary Problems in Analysis and Geometry by : Juan Gil

Download or read book Aspects of Boundary Problems in Analysis and Geometry written by Juan Gil and published by Birkhäuser. This book was released on 2012-12-06 with total page 574 pages. Available in PDF, EPUB and Kindle. Book excerpt: Boundary problems constitute an essential field of common mathematical interest, they lie in the center of research activities both in analysis and geometry. This book encompasses material from both disciplines, and focuses on their interactions which are particularly apparent in this field. Moreover, the survey style of the contributions makes the topics accessible to a broad audience with a background in analysis or geometry, and enables the reader to get a quick overview.

Quantum Field Theory: Batalin–Vilkovisky Formalism and Its Applications

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Author : Pavel Mnev
Publisher : American Mathematical Soc.
ISBN 13 : 1470452715
Total Pages : 200 pages
Book Rating : 4.4/5 (74 download)

Book Synopsis Quantum Field Theory: Batalin–Vilkovisky Formalism and Its Applications by : Pavel Mnev

Download or read book Quantum Field Theory: Batalin–Vilkovisky Formalism and Its Applications written by Pavel Mnev and published by American Mathematical Soc.. This book was released on 2019-08-20 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book originated from lecture notes for the course given by the author at the University of Notre Dame in the fall of 2016. The aim of the book is to give an introduction to the perturbative path integral for gauge theories (in particular, topological field theories) in Batalin–Vilkovisky formalism and to some of its applications. The book is oriented toward a graduate mathematical audience and does not require any prior physics background. To elucidate the picture, the exposition is mostly focused on finite-dimensional models for gauge systems and path integrals, while giving comments on what has to be amended in the infinite-dimensional case relevant to local field theory. Motivating examples discussed in the book include Alexandrov–Kontsevich–Schwarz–Zaboronsky sigma models, the perturbative expansion for Chern–Simons invariants of 3-manifolds given in terms of integrals over configurations of points on the manifold, the BF theory on cellular decompositions of manifolds, and Kontsevich's deformation quantization formula.

Fractal Geometry and Dynamical Systems in Pure and Applied Mathematics II

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Author : David Carfi
Publisher : American Mathematical Soc.
ISBN 13 : 0821891480
Total Pages : 384 pages
Book Rating : 4.8/5 (218 download)

Book Synopsis Fractal Geometry and Dynamical Systems in Pure and Applied Mathematics II by : David Carfi

Download or read book Fractal Geometry and Dynamical Systems in Pure and Applied Mathematics II written by David Carfi and published by American Mathematical Soc.. This book was released on 2013-10-24 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings from three conferences: the PISRS 2011 International Conference on Analysis, Fractal Geometry, Dynamical Systems and Economics, held November 8-12, 2011 in Messina, Italy; the AMS Special Session on Fractal Geometry in Pure and Applied Mathematics, in memory of Benoît Mandelbrot, held January 4-7, 2012, in Boston, MA; and the AMS Special Session on Geometry and Analysis on Fractal Spaces, held March 3-4, 2012, in Honolulu, HI. Articles in this volume cover fractal geometry and various aspects of dynamical systems in applied mathematics and the applications to other sciences. Also included are articles discussing a variety of connections between these subjects and various areas of physics, engineering, computer science, technology, economics and finance, as well as of mathematics (including probability theory in relation with statistical physics and heat kernel estimates, geometric measure theory, partial differential equations in relation with condensed matter physics, global analysis on non-smooth spaces, the theory of billiards, harmonic analysis and spectral geometry). The companion volume (Contemporary Mathematics, Volume 600) focuses on the more mathematical aspects of fractal geometry and dynamical systems.

Quantum Invariants

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Author : Tomotada Ohtsuki
Publisher : World Scientific
ISBN 13 : 9789812811172
Total Pages : 516 pages
Book Rating : 4.8/5 (111 download)

Book Synopsis Quantum Invariants by : Tomotada Ohtsuki

Download or read book Quantum Invariants written by Tomotada Ohtsuki and published by World Scientific. This book was released on 2002 with total page 516 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an extensive and self-contained presentation of quantum and related invariants of knots and 3-manifolds. Polynomial invariants of knots, such as the Jones and Alexander polynomials, are constructed as quantum invariants, i.e. invariants derived from representations of quantum groups and from the monodromy of solutions to the Knizhnik-Zamolodchikov equation. With the introduction of the Kontsevich invariant and the theory of Vassiliev invariants, the quantum invariants become well-organized. Quantum and perturbative invariants, the LMO invariant, and finite type invariants of 3-manifolds are discussed. The ChernOCoSimons field theory and the WessOCoZuminoOCoWitten model are described as the physical background of the invariants. Contents: Knots and Polynomial Invariants; Braids and Representations of the Braid Groups; Operator Invariants of Tangles via Sliced Diagrams; Ribbon Hopf Algebras and Invariants of Links; Monodromy Representations of the Braid Groups Derived from the KnizhnikOCoZamolodchikov Equation; The Kontsevich Invariant; Vassiliev Invariants; Quantum Invariants of 3-Manifolds; Perturbative Invariants of Knots and 3-Manifolds; The LMO Invariant; Finite Type Invariants of Integral Homology 3-Spheres. Readership: Researchers, lecturers and graduate students in geometry, topology and mathematical physics."

Path Integrals From Pev To Tev: 50 Years After Feynman's Paper - Proceedings Of The Sixth International Conference

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Author : Valerio Tognetti
Publisher : World Scientific
ISBN 13 : 9814543845
Total Pages : 642 pages
Book Rating : 4.8/5 (145 download)

Book Synopsis Path Integrals From Pev To Tev: 50 Years After Feynman's Paper - Proceedings Of The Sixth International Conference by : Valerio Tognetti

Download or read book Path Integrals From Pev To Tev: 50 Years After Feynman's Paper - Proceedings Of The Sixth International Conference written by Valerio Tognetti and published by World Scientific. This book was released on 1999-04-01 with total page 642 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains the invited contributions to the 6th International Conference on Path Integrals from peV to TeV, held in Florence in 1998. The conference, devoted to functional integration, brought together many physicists with interests ranging from elementary particles to nuclear, solid state, liquid state, polymer and complex systems physics. The variety of topics is reflected in the book, which is a unique collection of papers on manifold applications of functional methods in several areas of physics.

Asymptotic Expansions of Integrals

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Author : Norman Bleistein
Publisher : Courier Corporation
ISBN 13 : 0486650820
Total Pages : 453 pages
Book Rating : 4.4/5 (866 download)

Book Synopsis Asymptotic Expansions of Integrals by : Norman Bleistein

Download or read book Asymptotic Expansions of Integrals written by Norman Bleistein and published by Courier Corporation. This book was released on 1986-01-01 with total page 453 pages. Available in PDF, EPUB and Kindle. Book excerpt: Excellent introductory text, written by two experts, presents a coherent and systematic view of principles and methods. Topics include integration by parts, Watson's lemma, LaPlace's method, stationary phase, and steepest descents. Additional subjects include the Mellin transform method and less elementary aspects of the method of steepest descents. 1975 edition.

Symplectic Manifolds and Jones-Witten Theory

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Author : S. K. Donaldson
Publisher : Cambridge University Press
ISBN 13 : 9780521400015
Total Pages : 264 pages
Book Rating : 4.4/5 ( download)

Book Synopsis Symplectic Manifolds and Jones-Witten Theory by : S. K. Donaldson

Download or read book Symplectic Manifolds and Jones-Witten Theory written by S. K. Donaldson and published by Cambridge University Press. This book was released on 1990 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Sir Michael Atiyah

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Author : Michael Francis Atiyah
Publisher : American Mathematical Society(RI)
ISBN 13 :
Total Pages : 416 pages
Book Rating : 4.3/5 (91 download)

Book Synopsis Sir Michael Atiyah by : Michael Francis Atiyah

Download or read book Sir Michael Atiyah written by Michael Francis Atiyah and published by American Mathematical Society(RI). This book was released on 1998 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt: A concis, yet comprehensive introduction to the contemporary politics of Latin America, this book focuses on the enduring difficulties of achieving democratic stability. It explores the conduct of government through classic concepts like authority, accountability, and participation. These themes are developed within a comparative perspective.

Moduli Spaces of Riemannian Metrics

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Author : Wilderich Tuschmann
Publisher : Springer
ISBN 13 : 3034809484
Total Pages : 127 pages
Book Rating : 4.0/5 (348 download)

Book Synopsis Moduli Spaces of Riemannian Metrics by : Wilderich Tuschmann

Download or read book Moduli Spaces of Riemannian Metrics written by Wilderich Tuschmann and published by Springer. This book was released on 2015-10-14 with total page 127 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book studies certain spaces of Riemannian metrics on both compact and non-compact manifolds. These spaces are defined by various sign-based curvature conditions, with special attention paid to positive scalar curvature and non-negative sectional curvature, though we also consider positive Ricci and non-positive sectional curvature. If we form the quotient of such a space of metrics under the action of the diffeomorphism group (or possibly a subgroup) we obtain a moduli space. Understanding the topology of both the original space of metrics and the corresponding moduli space form the central theme of this book. For example, what can be said about the connectedness or the various homotopy groups of such spaces? We explore the major results in the area, but provide sufficient background so that a non-expert with a grounding in Riemannian geometry can access this growing area of research.

Operators, Geometry and Quanta

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Author : Dmitri Fursaev
Publisher : Springer Science & Business Media
ISBN 13 : 9400702051
Total Pages : 294 pages
Book Rating : 4.4/5 (7 download)

Book Synopsis Operators, Geometry and Quanta by : Dmitri Fursaev

Download or read book Operators, Geometry and Quanta written by Dmitri Fursaev and published by Springer Science & Business Media. This book was released on 2011-06-25 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives a detailed and self-contained introduction into the theory of spectral functions, with an emphasis on their applications to quantum field theory. All methods are illustrated with applications to specific physical problems from the forefront of current research, such as finite-temperature field theory, D-branes, quantum solitons and noncommutativity. In the first part of the book, necessary background information on differential geometry and quantization, including less standard material, is collected. The second part of the book contains a detailed description of main spectral functions and methods of their calculation. In the third part, the theory is applied to several examples (D-branes, quantum solitons, anomalies, noncommutativity). This book addresses advanced graduate students and researchers in mathematical physics with basic knowledge of quantum field theory and differential geometry. The aim is to prepare readers to use spectral functions in their own research, in particular in relation to heat kernels and zeta functions.

The Maz'ya Anniversary Collection

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Author : Jürgen Rossmann
Publisher : Springer Science & Business Media
ISBN 13 : 9783764362010
Total Pages : 384 pages
Book Rating : 4.3/5 (62 download)

Book Synopsis The Maz'ya Anniversary Collection by : Jürgen Rossmann

Download or read book The Maz'ya Anniversary Collection written by Jürgen Rossmann and published by Springer Science & Business Media. This book was released on 1999 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first volume of a collection of articles dedicated to V.G Maz'ya on the occasion of his 60th birthday. It contains surveys on his work in different fields of mathematics or on areas to which he made essential contributions. Other articles of this book have their origin in the common work with Maz'ya. V.G Maz'ya is author or co-author of more than 300 scientific works on various fields of functional analysis, function theory, numerical analysis, partial differential equations and their application. The reviews in this book show his enormous productivity and the large variety of his work. The scond volume contains most of the invited lectures of the Conference on Functional Analysis, Partial Differential Equations and Applications held in Rostock in September 1998 in honor of V.G Maz'ya. Here different problems of functional analysis, potential theory, linear and nonlinear partial differential equations, theory of function spaces and numerical analysis are treated. The authors, who are outstanding experts in these fields, present surveys as well as new results.

The Asian Journal of Mathematics

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Author :
Publisher :
ISBN 13 :
Total Pages : 616 pages
Book Rating : 4.3/5 (91 download)

Book Synopsis The Asian Journal of Mathematics by :

Download or read book The Asian Journal of Mathematics written by and published by . This book was released on 1998 with total page 616 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Principles Of Applied Mathematics

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Author : James P. Keener
Publisher : CRC Press
ISBN 13 : 0429972067
Total Pages : 624 pages
Book Rating : 4.4/5 (299 download)

Book Synopsis Principles Of Applied Mathematics by : James P. Keener

Download or read book Principles Of Applied Mathematics written by James P. Keener and published by CRC Press. This book was released on 2019-05-20 with total page 624 pages. Available in PDF, EPUB and Kindle. Book excerpt: Principles of Applied Mathematics provides a comprehensive look at how classical methods are used in many fields and contexts. Updated to reflect developments of the last twenty years, it shows how two areas of classical applied mathematics spectral theory of operators and asymptotic analysis are useful for solving a wide range of applied science problems. Topics such as asymptotic expansions, inverse scattering theory, and perturbation methods are combined in a unified way with classical theory of linear operators. Several new topics, including wavelength analysis, multigrid methods, and homogenization theory, are blended into this mix to amplify this theme.This book is ideal as a survey course for graduate students in applied mathematics and theoretically oriented engineering and science students. This most recent edition, for the first time, now includes extensive corrections collated and collected by the author.

Physics Briefs

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Author :
Publisher :
ISBN 13 :
Total Pages : 1256 pages
Book Rating : 4.3/5 (91 download)

Book Synopsis Physics Briefs by :

Download or read book Physics Briefs written by and published by . This book was released on 1994 with total page 1256 pages. Available in PDF, EPUB and Kindle. Book excerpt: