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Heat Kernel Method and its Applications

Author: Ivan Avramidi

Publisher: Birkhäuser

Published: 2015-11-26

Total Pages: 402

ISBN-13: 3319262661

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The heart of the book is the development of a short-time asymptotic expansion for the heat kernel. This is explained in detail and explicit examples of some advanced calculations are given. In addition some advanced methods and extensions, including path integrals, jump diffusion and others are presented. The book consists of four parts: Analysis, Geometry, Perturbations and Applications. The first part shortly reviews of some background material and gives an introduction to PDEs. The second part is devoted to a short introduction to various aspects of differential geometry that will be needed later. The third part and heart of the book presents a systematic development of effective methods for various approximation schemes for parabolic differential equations. The last part is devoted to applications in financial mathematics, in particular, stochastic differential equations. Although this book is intended for advanced undergraduate or beginning graduate students in, it should also provide a useful reference for professional physicists, applied mathematicians as well as quantitative analysts with an interest in PDEs.

Book Synopsis Heat Kernel Method and its Applications by : Ivan Avramidi

Download or read book Heat Kernel Method and its Applications written by Ivan Avramidi and published by Birkhäuser. This book was released on 2015-11-26 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: The heart of the book is the development of a short-time asymptotic expansion for the heat kernel. This is explained in detail and explicit examples of some advanced calculations are given. In addition some advanced methods and extensions, including path integrals, jump diffusion and others are presented. The book consists of four parts: Analysis, Geometry, Perturbations and Applications. The first part shortly reviews of some background material and gives an introduction to PDEs. The second part is devoted to a short introduction to various aspects of differential geometry that will be needed later. The third part and heart of the book presents a systematic development of effective methods for various approximation schemes for parabolic differential equations. The last part is devoted to applications in financial mathematics, in particular, stochastic differential equations. Although this book is intended for advanced undergraduate or beginning graduate students in, it should also provide a useful reference for professional physicists, applied mathematicians as well as quantitative analysts with an interest in PDEs.

Heat Kernel on Lie Groups and Maximally Symmetric Spaces

Author: Ivan G. Avramidi

Publisher: Springer Nature

Published: 2023-05-27

Total Pages: 197

ISBN-13: 3031274512

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This monograph studies the heat kernel for the spin-tensor Laplacians on Lie groups and maximally symmetric spaces. It introduces many original ideas, methods, and tools developed by the author and provides a list of all known exact results in explicit form – and derives them – for the heat kernel on spheres and hyperbolic spaces. Part I considers the geometry of simple Lie groups and maximally symmetric spaces in detail, and Part II discusses the calculation of the heat kernel for scalar, spinor, and generic Laplacians on spheres and hyperbolic spaces in various dimensions. This text will be a valuable resource for researchers and graduate students working in various areas of mathematics – such as global analysis, spectral geometry, stochastic processes, and financial mathematics – as well in areas of mathematical and theoretical physics – including quantum field theory, quantum gravity, string theory, and statistical physics.

Book Synopsis Heat Kernel on Lie Groups and Maximally Symmetric Spaces by : Ivan G. Avramidi

Download or read book Heat Kernel on Lie Groups and Maximally Symmetric Spaces written by Ivan G. Avramidi and published by Springer Nature. This book was released on 2023-05-27 with total page 197 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph studies the heat kernel for the spin-tensor Laplacians on Lie groups and maximally symmetric spaces. It introduces many original ideas, methods, and tools developed by the author and provides a list of all known exact results in explicit form – and derives them – for the heat kernel on spheres and hyperbolic spaces. Part I considers the geometry of simple Lie groups and maximally symmetric spaces in detail, and Part II discusses the calculation of the heat kernel for scalar, spinor, and generic Laplacians on spheres and hyperbolic spaces in various dimensions. This text will be a valuable resource for researchers and graduate students working in various areas of mathematics – such as global analysis, spectral geometry, stochastic processes, and financial mathematics – as well in areas of mathematical and theoretical physics – including quantum field theory, quantum gravity, string theory, and statistical physics.

Heat Kernels for Elliptic and Sub-elliptic Operators

Author: Ovidiu Calin

Publisher: Springer Science & Business Media

Published: 2010-10-10

Total Pages: 436

ISBN-13: 0817649956

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This monograph is a unified presentation of several theories of finding explicit formulas for heat kernels for both elliptic and sub-elliptic operators. These kernels are important in the theory of parabolic operators because they describe the distribution of heat on a given manifold as well as evolution phenomena and diffusion processes. Heat Kernels for Elliptic and Sub-elliptic Operators is an ideal reference for graduate students, researchers in pure and applied mathematics, and theoretical physicists interested in understanding different ways of approaching evolution operators.

Book Synopsis Heat Kernels for Elliptic and Sub-elliptic Operators by : Ovidiu Calin

Download or read book Heat Kernels for Elliptic and Sub-elliptic Operators written by Ovidiu Calin and published by Springer Science & Business Media. This book was released on 2010-10-10 with total page 436 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is a unified presentation of several theories of finding explicit formulas for heat kernels for both elliptic and sub-elliptic operators. These kernels are important in the theory of parabolic operators because they describe the distribution of heat on a given manifold as well as evolution phenomena and diffusion processes. Heat Kernels for Elliptic and Sub-elliptic Operators is an ideal reference for graduate students, researchers in pure and applied mathematics, and theoretical physicists interested in understanding different ways of approaching evolution operators.

Introduction to Quantum Field Theory with Applications to Quantum Gravity

Author: Iosif L. Buchbinder

Publisher: Oxford University Press, USA

Published: 2021-03

Total Pages: 536

ISBN-13: 019883831X

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This textbook presents a detailed introduction to the general concepts of quantum field theory, with special emphasis on principal aspects of functional methods and renormalization in gauge theories, and includes an introduction to semiclassical and perturbative quantum gravity in flat and curved spacetimes.

Book Synopsis Introduction to Quantum Field Theory with Applications to Quantum Gravity by : Iosif L. Buchbinder

Download or read book Introduction to Quantum Field Theory with Applications to Quantum Gravity written by Iosif L. Buchbinder and published by Oxford University Press, USA. This book was released on 2021-03 with total page 536 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook presents a detailed introduction to the general concepts of quantum field theory, with special emphasis on principal aspects of functional methods and renormalization in gauge theories, and includes an introduction to semiclassical and perturbative quantum gravity in flat and curved spacetimes.

Proceedings Of The Julian Schwinger Centennial Conference

Author: Englert Berthold-georg

Publisher: World Scientific

Published: 2019-10-30

Total Pages: 336

ISBN-13: 9811213151

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The Julian Schwinger Centennial Conference of 2018 assembled many of Schwinger's students, colleagues, and friends to celebrate this towering figure of twentieth century physics one hundred years after his birth. This proceedings volume collects talks delivered on this occasion. They cover a wide range of topics, all related to Schwinger's rich scientific legacy — supplemented by personal recollections about Julian Schwinger, the physicist, the teacher, and the gentleman.Also included are an essay of 1985, co-authored by Schwinger but not published previously, as well as the transcripts of speeches by distinguished colleagues at the 1978 gathering when Schwinger's sixtieth birthday was celebrated.

Book Synopsis Proceedings Of The Julian Schwinger Centennial Conference by : Englert Berthold-georg

Download or read book Proceedings Of The Julian Schwinger Centennial Conference written by Englert Berthold-georg and published by World Scientific. This book was released on 2019-10-30 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Julian Schwinger Centennial Conference of 2018 assembled many of Schwinger's students, colleagues, and friends to celebrate this towering figure of twentieth century physics one hundred years after his birth. This proceedings volume collects talks delivered on this occasion. They cover a wide range of topics, all related to Schwinger's rich scientific legacy — supplemented by personal recollections about Julian Schwinger, the physicist, the teacher, and the gentleman.Also included are an essay of 1985, co-authored by Schwinger but not published previously, as well as the transcripts of speeches by distinguished colleagues at the 1978 gathering when Schwinger's sixtieth birthday was celebrated.

Journal of Mathematical Sciences, the University of Tokyo

Author:

Publisher:

Published: 2004

Total Pages: 534

ISBN-13:

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Book Synopsis Journal of Mathematical Sciences, the University of Tokyo by :

Download or read book Journal of Mathematical Sciences, the University of Tokyo written by and published by . This book was released on 2004 with total page 534 pages. Available in PDF, EPUB and Kindle. Book excerpt:

The Method of Layer Potentials for the Heat Equation in Time-Varying Domains

Author: John L. Lewis

Publisher: American Mathematical Soc.

Published: 1995

Total Pages: 170

ISBN-13: 0821803603

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This memoir consists of three papers in which we develop the method of layer potentials for the heat equation in time-varying domains. In Chapter I we show certain singular integral operators on [italic]L[superscript italic]p are bounded. in Chapter II, we develop a modification of the David buildup scheme to obtain [italic]L[superscript italic]p boundedness of the double layer heat potential on the boundary of our domains. In Chapter III, we use the results of the first two chapters to show the mutual absolute continuity of parabolic measure and a certain projective Lebesgue measure.

Book Synopsis The Method of Layer Potentials for the Heat Equation in Time-Varying Domains by : John L. Lewis

Download or read book The Method of Layer Potentials for the Heat Equation in Time-Varying Domains written by John L. Lewis and published by American Mathematical Soc.. This book was released on 1995 with total page 170 pages. Available in PDF, EPUB and Kindle. Book excerpt: This memoir consists of three papers in which we develop the method of layer potentials for the heat equation in time-varying domains. In Chapter I we show certain singular integral operators on [italic]L[superscript italic]p are bounded. in Chapter II, we develop a modification of the David buildup scheme to obtain [italic]L[superscript italic]p boundedness of the double layer heat potential on the boundary of our domains. In Chapter III, we use the results of the first two chapters to show the mutual absolute continuity of parabolic measure and a certain projective Lebesgue measure.

The Heat Kernel Lefschetz Fixed Point Formula for the Spin-c Dirac Operator

Author: J.J. Duistermaat

Publisher: Springer Science & Business Media

Published: 2013-12-01

Total Pages: 245

ISBN-13: 1461253446

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When visiting M.I.T. for two weeks in October 1994, Victor Guillemin made me enthusiastic about a problem in symplectic geometry which involved the use of the so-called spin-c Dirac operator. Back in Berkeley, where I had l spent a sabbatical semester , I tried to understand the basic facts about this operator: its definition, the main theorems about it, and their proofs. This book is an outgrowth of the notes in which I worked this out. For me this was a great learning experience because of the many beautiful mathematical structures which are involved. I thank the Editorial Board of Birkhauser, especially Haim Brezis, for sug gesting the publication of these notes as a book. I am also very grateful for the suggestions by the referees, which have led to substantial improvements in the presentation. Finally I would like to express special thanks to Ann Kostant for her help and her prodding me, in her charming way, into the right direction. J.J. Duistermaat Utrecht, October 16, 1995.

Book Synopsis The Heat Kernel Lefschetz Fixed Point Formula for the Spin-c Dirac Operator by : J.J. Duistermaat

Download or read book The Heat Kernel Lefschetz Fixed Point Formula for the Spin-c Dirac Operator written by J.J. Duistermaat and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 245 pages. Available in PDF, EPUB and Kindle. Book excerpt: When visiting M.I.T. for two weeks in October 1994, Victor Guillemin made me enthusiastic about a problem in symplectic geometry which involved the use of the so-called spin-c Dirac operator. Back in Berkeley, where I had l spent a sabbatical semester , I tried to understand the basic facts about this operator: its definition, the main theorems about it, and their proofs. This book is an outgrowth of the notes in which I worked this out. For me this was a great learning experience because of the many beautiful mathematical structures which are involved. I thank the Editorial Board of Birkhauser, especially Haim Brezis, for sug gesting the publication of these notes as a book. I am also very grateful for the suggestions by the referees, which have led to substantial improvements in the presentation. Finally I would like to express special thanks to Ann Kostant for her help and her prodding me, in her charming way, into the right direction. J.J. Duistermaat Utrecht, October 16, 1995.

Heat Kernel and Quantum Gravity

Author: Ivan G. Avramidi

Publisher: Springer Science & Business Media

Published: 2003-07-01

Total Pages: 153

ISBN-13: 3540465235

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This book tackles quantum gravity via the so-called background field method and its effective action functional. The author presents an explicitly covariant and effective technique to calculate the de Witt coefficients and to analyze the Schwinger-de Wit asymptotic expansion of the effective action. He also investigates the ultraviolet behaviour of higher-derivative quantum gravity. The book addresses theoretical physicists, graduate students as well as researchers, but should also be of interest to physicists working in mathematical or elementary particle physics.

Book Synopsis Heat Kernel and Quantum Gravity by : Ivan G. Avramidi

Download or read book Heat Kernel and Quantum Gravity written by Ivan G. Avramidi and published by Springer Science & Business Media. This book was released on 2003-07-01 with total page 153 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book tackles quantum gravity via the so-called background field method and its effective action functional. The author presents an explicitly covariant and effective technique to calculate the de Witt coefficients and to analyze the Schwinger-de Wit asymptotic expansion of the effective action. He also investigates the ultraviolet behaviour of higher-derivative quantum gravity. The book addresses theoretical physicists, graduate students as well as researchers, but should also be of interest to physicists working in mathematical or elementary particle physics.

The Ubiquitous Heat Kernel

Author: Jay Jorgenson

Publisher: American Mathematical Soc.

Published: 2006

Total Pages: 410

ISBN-13: 0821836986

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The aim of this volume is to bring together research ideas from various fields of mathematics which utilize the heat kernel or heat kernel techniques in their research. The intention of this collection of papers is to broaden productive communication across mathematical sub-disciplines and to provide a vehicle which would allow experts in one field to initiate research with individuals in another field, as well as to give non-experts a resource which can facilitate expanding theirresearch and connecting with others.

Book Synopsis The Ubiquitous Heat Kernel by : Jay Jorgenson

Download or read book The Ubiquitous Heat Kernel written by Jay Jorgenson and published by American Mathematical Soc.. This book was released on 2006 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this volume is to bring together research ideas from various fields of mathematics which utilize the heat kernel or heat kernel techniques in their research. The intention of this collection of papers is to broaden productive communication across mathematical sub-disciplines and to provide a vehicle which would allow experts in one field to initiate research with individuals in another field, as well as to give non-experts a resource which can facilitate expanding theirresearch and connecting with others.