Lectures On Gaussian Integral Operators And Classical Groups

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Lectures on Gaussian Integral Operators and Classical Groups

Yu. A. Neretin
Lectures on Gaussian Integral Operators and Classical Groups Book PDF

Author : Yu. A. Neretin
Publisher : European Mathematical Society
Page : 576 pages
File Size : 54,7 Mb
Release : 2011
Category : Geometry, Differential
ISBN : 3037190809

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Lectures on Gaussian Integral Operators and Classical Groups by Yu. A. Neretin Pdf

This book is an elementary self-contained introduction to some constructions of representation theory and related topics of differential geometry and analysis. Topics covered include the theory of various Fourier-like integral operators such as Segal-Bargmann transforms, Gaussian integral operators in $L^2$ and in the Fock space, integral operators with theta-kernels, the geometry of real and $p$-adic classical groups and symmetric spaces. The heart of the book is the Weil representation of the symplectic group (real and complex realizations, relations with theta-functions and modular forms, $p$-adic and adelic constructions) and representations in Hilbert spaces of holomorphic functions of several complex variables. This book is addressed to graduate students and researchers in representation theory, differential geometry, and operator theory. Prerequisites are standard university courses in linear algebra, functional analysis, and complex analysis.

Lectures on Gaussian Integral Operators and Classical Groups

YURII A. NERETIN.,Yu. A. Neretin
Lectures on Gaussian Integral Operators and Classical Groups Book PDF

Author : YURII A. NERETIN.,Yu. A. Neretin
Publisher : Unknown
Page : 559 pages
File Size : 43,6 Mb
Release : 2024-06-23
Category : Geometry, Differential
ISBN : 3037195800

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Lectures on Gaussian Integral Operators and Classical Groups by YURII A. NERETIN.,Yu. A. Neretin Pdf

This book is an elementary self-contained introduction to some constructions of representation theory and related topics of differential geometry and analysis. Topics covered include the theory of various Fourier-like integral operators as Segal-Bargmann transforms, Gaussian integral operators in $L^2$ and in the Fock space, integral operators with theta-kernels, the geometry of real and $p$-adic classical groups and symmetric spaces. The heart of the book is the Weil representation of the symplectic group (real and complex realizations, relations with theta-functions and modular forms, $p$-adic and adelic constructions) and representations in Hilbert spaces of holomorphic functions of several complex variables. The book is addressed to graduate students and researchers in representation theory, differential geometry, and operator theory. The reader is supposed to be familiar with standard university courses in linear algebra, functional analysis, and complex analysis.

Quantum Theory, Groups and Representations

Peter Woit
Quantum Theory Groups and Representations Book PDF

Author : Peter Woit
Publisher : Springer
Page : 668 pages
File Size : 49,7 Mb
Release : 2017-11-01
Category : Science
ISBN : 9783319646121

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Quantum Theory, Groups and Representations by Peter Woit Pdf

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.

Faber Systems and Their Use in Sampling, Discrepancy, Numerical Integration

Hans Triebel
Faber Systems and Their Use in Sampling Discrepancy Numerical Integration Book PDF

Author : Hans Triebel
Publisher : European Mathematical Society
Page : 120 pages
File Size : 54,7 Mb
Release : 2012
Category : Function spaces
ISBN : 3037191074

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Faber Systems and Their Use in Sampling, Discrepancy, Numerical Integration by Hans Triebel Pdf

This book deals first with Haar bases, Faber bases and Faber frames for weighted function spaces on the real line and the plane. It extends results in the author's book, ``Bases in Function Spaces, Sampling, Discrepancy, Numerical Integration'' (EMS, 2010), from unweighted spaces (preferably in cubes) to weighted spaces. The obtained assertions are used to study sampling and numerical integration in weighted spaces on the real line and weighted spaces with dominating mixed smoothness in the plane. A short chapter deals with the discrepancy for spaces on intervals.

Lectures on Duflo Isomorphisms in Lie Algebra and Complex Geometry

Damien Calaque,Carlo Antonio Rossi
Lectures on Duflo Isomorphisms in Lie Algebra and Complex Geometry Book PDF

Author : Damien Calaque,Carlo Antonio Rossi
Publisher : European Mathematical Society
Page : 120 pages
File Size : 49,7 Mb
Release : 2011
Category : Cohomology operations
ISBN : 3037190965

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Lectures on Duflo Isomorphisms in Lie Algebra and Complex Geometry by Damien Calaque,Carlo Antonio Rossi Pdf

The Duflo isomorphism first appeared in Lie theory and representation theory. It is an isomorphism between invariant polynomials of a Lie algebra and the center of its universal enveloping algebra, generalizing the pioneering work of Harish-Chandra on semi-simple Lie algebras. Kontsevich later refined Duflo's result in the framework of deformation quantization and also observed that there is a similar isomorphism between Dolbeault cohomology of holomorphic polyvector fields on a complex manifold and its Hochschild cohomology. This book, which arose from a series of lectures by Damien Calaque at ETH, derives these two isomorphisms from a Duflo-type result for $Q$-manifolds. All notions mentioned above are introduced and explained in this book. The only prerequisites are basic linear algebra and differential geometry. In addition to standard notions such as Lie (super) algebras, complex manifolds, Hochschild and Chevalley-Eilenberg cohomologies, spectral sequences, Atiyah and Todd classes, the graphical calculus introduced by Kontsevich in his seminal work on deformation quantization is addressed in detail. This book is well suited for graduate students in mathematics and mathematical physics as well as researchers working in Lie theory, algebraic geometry, and deformation theory.

A Course on Elation Quadrangles

Koen Thas
A Course on Elation Quadrangles Book PDF

Author : Koen Thas
Publisher : European Mathematical Society
Page : 136 pages
File Size : 41,5 Mb
Release : 2012
Category : Abelian p-groups
ISBN : 3037191104

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A Course on Elation Quadrangles by Koen Thas Pdf

The notion of elation generalized quadrangle is a natural generalization to the theory of generalized quadrangles of the important notion of translation planes in the theory of projective planes. Almost any known class of finite generalized quadrangles can be constructed from a suitable class of elation quadrangles. In this book the author considers several aspects of the theory of elation generalized quadrangles. Special attention is given to local Moufang conditions on the foundational level, exploring, for instance, Knarr's question from the 1990s concerning the very notion of elation quadrangles. All the known results on Kantor's prime power conjecture for finite elation quadrangles are gathered, some of them published here for the first time. The structural theory of elation quadrangles and their groups is heavily emphasized. Other related topics, such as $p$-modular cohomology, Heisenberg groups, and existence problems for certain translation nets, are briefly touched. This book starts from scratch and is essentially self-contained. Many alternative proofs are given for known theorems. This course contains dozens of exercises at various levels, from very easy to rather difficult, and will stimulate undergraduate and graduate students to enter the fascinating and rich world of elation quadrangles. More accomplished mathematicians will find the final chapters especially challenging.

Representation Theory, Complex Analysis, and Integral Geometry

Bernhard Krötz,Omer Offen,Eitan Sayag
Representation Theory Complex Analysis and Integral Geometry Book PDF

Author : Bernhard Krötz,Omer Offen,Eitan Sayag
Publisher : Springer Science & Business Media
Page : 282 pages
File Size : 45,7 Mb
Release : 2011-12-13
Category : Mathematics
ISBN : 9780817648169

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Representation Theory, Complex Analysis, and Integral Geometry by Bernhard Krötz,Omer Offen,Eitan Sayag Pdf

This volume targets graduate students and researchers in the fields of representation theory, automorphic forms, Hecke algebras, harmonic analysis, number theory.

Mathematical Foundations of Supersymmetry

Claudio Carmeli,Lauren Caston,Rita Fioresi
Mathematical Foundations of Supersymmetry Book PDF

Author : Claudio Carmeli,Lauren Caston,Rita Fioresi
Publisher : European Mathematical Society
Page : 308 pages
File Size : 42,6 Mb
Release : 2011
Category : Lie algebras
ISBN : 3037190973

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Mathematical Foundations of Supersymmetry by Claudio Carmeli,Lauren Caston,Rita Fioresi Pdf

Supersymmetry is a highly active area of considerable interest among physicists and mathematicians. It is not only fascinating in its own right, but there is also indication that it plays a fundamental role in the physics of elementary particles and gravitation. The purpose of the book is to lay down the foundations of the subject, providing the reader with a comprehensive introduction to the language and techniques, as well as detailed proofs and many clarifying examples. This book is aimed ideally at second-year graduate students. After the first three introductory chapters, the text is divided into two parts: the theory of smooth supermanifolds and Lie supergroups, including the Frobenius theorem, and the theory of algebraic superschemes and supergroups. There are three appendices. The first introduces Lie superalgebras and representations of classical Lie superalgebras, the second collects some relevant facts on categories, sheafification of functors and commutative algebra, and the third explains the notion of Frechet space in the super context.

Beyond Pseudo-Rotations in Pseudo-Euclidean Spaces

Abraham Ungar
Beyond Pseudo Rotations in Pseudo Euclidean Spaces Book PDF

Author : Abraham Ungar
Publisher : Academic Press
Page : 418 pages
File Size : 47,9 Mb
Release : 2018-01-10
Category : Mathematics
ISBN : 9780128117743

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Beyond Pseudo-Rotations in Pseudo-Euclidean Spaces by Abraham Ungar Pdf

Beyond Pseudo-Rotations in Pseudo-Euclidean Spaces presents for the first time a unified study of the Lorentz transformation group SO(m, n) of signature (m, n), m, n ∈ N, which is fully analogous to the Lorentz group SO(1, 3) of Einstein’s special theory of relativity. It is based on a novel parametric realization of pseudo-rotations by a vector-like parameter with two orientation parameters. The book is of interest to specialized researchers in the areas of algebra, geometry and mathematical physics, containing new results that suggest further exploration in these areas. Introduces the study of generalized gyrogroups and gyrovector spaces Develops new algebraic structures, bi-gyrogroups and bi-gyrovector spaces Helps readers to surmount boundaries between algebra, geometry and physics Assists readers to parametrize and describe the full set of generalized Lorentz transformations in a geometric way Generalizes approaches from gyrogroups and gyrovector spaces to bi-gyrogroups and bi-gyrovector spaces with geometric entanglement

Singularities in Geometry, Topology, Foliations and Dynamics

José Luis Cisneros-Molina,Dũng Tráng Lê,Mutsuo Oka,Jawad Snoussi
Singularities in Geometry Topology Foliations and Dynamics Book PDF

Author : José Luis Cisneros-Molina,Dũng Tráng Lê,Mutsuo Oka,Jawad Snoussi
Publisher : Birkhäuser
Page : 231 pages
File Size : 51,6 Mb
Release : 2017-02-13
Category : Mathematics
ISBN : 9783319393391

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Singularities in Geometry, Topology, Foliations and Dynamics by José Luis Cisneros-Molina,Dũng Tráng Lê,Mutsuo Oka,Jawad Snoussi Pdf

This book features state-of-the-art research on singularities in geometry, topology, foliations and dynamics and provides an overview of the current state of singularity theory in these settings. Singularity theory is at the crossroad of various branches of mathematics and science in general. In recent years there have been remarkable developments, both in the theory itself and in its relations with other areas. The contributions in this volume originate from the “Workshop on Singularities in Geometry, Topology, Foliations and Dynamics”, held in Merida, Mexico, in December 2014, in celebration of José Seade’s 60th Birthday. It is intended for researchers and graduate students interested in singularity theory and its impact on other fields.

An Advanced Complex Analysis Problem Book

Daniel Alpay
An Advanced Complex Analysis Problem Book Book PDF

Author : Daniel Alpay
Publisher : Birkhäuser
Page : 521 pages
File Size : 42,7 Mb
Release : 2015-11-13
Category : Mathematics
ISBN : 9783319160597

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An Advanced Complex Analysis Problem Book by Daniel Alpay Pdf

This is an exercises book at the beginning graduate level, whose aim is to illustrate some of the connections between functional analysis and the theory of functions of one variable. A key role is played by the notions of positive definite kernel and of reproducing kernel Hilbert space. A number of facts from functional analysis and topological vector spaces are surveyed. Then, various Hilbert spaces of analytic functions are studied.

Coherent Quantum Physics

Arnold Neumaier
Coherent Quantum Physics Book PDF

Author : Arnold Neumaier
Publisher : Walter de Gruyter GmbH & Co KG
Page : 301 pages
File Size : 43,6 Mb
Release : 2019-10-21
Category : Science
ISBN : 9783110667387

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Coherent Quantum Physics by Arnold Neumaier Pdf

This book introduces mathematicians, physicists, and philosophers to a new, coherent approach to theory and interpretation of quantum physics, in which classical and quantum thinking live peacefully side by side and jointly fertilize the intuition. The formal, mathematical core of quantum physics is cleanly separated from the interpretation issues. The book demonstrates that the universe can be rationally and objectively understood from the smallest to the largest levels of modeling. The thermal interpretation featured in this book succeeds without any change in the theory. It involves one radical step, the reinterpretation of an assumption that was virtually never questioned before - the traditional eigenvalue link between theory and observation is replaced by a q-expectation link: Objective properties are given by q-expectations of products of quantum fields and what is computable from these. Averaging over macroscopic spacetime regions produces macroscopic quantities with negligible uncertainty, and leads to classical physics. - Reflects the actual practice of quantum physics. - Models the quantum-classical interface through coherent spaces. - Interprets both quantum mechanics and quantum field theory. - Eliminates probability and measurement from the foundations. - Proposes a novel solution of the measurement problem.

Hypersymmetry

György Darvas
Hypersymmetry Book PDF

Author : György Darvas
Publisher : Walter de Gruyter GmbH & Co KG
Page : 228 pages
File Size : 48,8 Mb
Release : 2020-12-16
Category : Science
ISBN : 9783110713183

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Hypersymmetry by György Darvas Pdf

The book describes how field-charges, split into isotopic pairs, can commute and identifies the group of transformations that governs this exchange between their states. Invariance under this group is defined as Hypersymmetry. The book develops the physical consequences of Hypersymmetry such as conserved property, quanta and mediating bosons of the interaction field. Since all this expands beyond the standard model, the work determines the energy limits of the applicability of Hypersymmetry and discusses, how to remove the unwanted mass of the predicted set of bosons. Finally, it presents how the model can be applied in the four fundamental interactions. • Comprehensive work covering recent research. • Detailed calculations for a step by step understanding. • Useful reading for master students and researchers in theoretical and experimental physics. • A practical textbook for courses on the physics of the isotopic field-charges, their conservation and interactions.

Real Analysis: A Comprehensive Course in Analysis, Part 1

Barry Simon
Real Analysis A Comprehensive Course in Analysis Part 1 Book PDF

Author : Barry Simon
Publisher : American Mathematical Soc.
Page : 789 pages
File Size : 52,5 Mb
Release : 2015-11-02
Category : Mathematical analysis
ISBN : 9781470410995

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Real Analysis: A Comprehensive Course in Analysis, Part 1 by Barry Simon Pdf

A Comprehensive Course in Analysis by Poincaré Prize winner Barry Simon is a five-volume set that can serve as a graduate-level analysis textbook with a lot of additional bonus information, including hundreds of problems and numerous notes that extend the text and provide important historical background. Depth and breadth of exposition make this set a valuable reference source for almost all areas of classical analysis. Part 1 is devoted to real analysis. From one point of view, it presents the infinitesimal calculus of the twentieth century with the ultimate integral calculus (measure theory) and the ultimate differential calculus (distribution theory). From another, it shows the triumph of abstract spaces: topological spaces, Banach and Hilbert spaces, measure spaces, Riesz spaces, Polish spaces, locally convex spaces, Fréchet spaces, Schwartz space, and spaces. Finally it is the study of big techniques, including the Fourier series and transform, dual spaces, the Baire category, fixed point theorems, probability ideas, and Hausdorff dimension. Applications include the constructions of nowhere differentiable functions, Brownian motion, space-filling curves, solutions of the moment problem, Haar measure, and equilibrium measures in potential theory.

Geometric Methods in Physics

Piotr Kielanowski,S. Twareque Ali,Anatol Odzijewicz,Martin Schlichenmaier,Theodore Voronov
Geometric Methods in Physics Book PDF

Author : Piotr Kielanowski,S. Twareque Ali,Anatol Odzijewicz,Martin Schlichenmaier,Theodore Voronov
Publisher : Springer Science & Business Media
Page : 432 pages
File Size : 49,6 Mb
Release : 2012-11-05
Category : Mathematics
ISBN : 9783034804486

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Geometric Methods in Physics by Piotr Kielanowski,S. Twareque Ali,Anatol Odzijewicz,Martin Schlichenmaier,Theodore Voronov Pdf

The Białowieża workshops on Geometric Methods in Physics are among the most important meetings in the field. Every year some 80 to 100 participants from both mathematics and physics join to discuss new developments and to interchange ideas. This volume contains contributions by selected speakers at the XXX meeting in 2011 as well as additional review articles and shows that the workshop remains at the cutting edge of ongoing research. The 2011 workshop focussed on the works of the late Felix A. Berezin (1931–1980) on the occasion of his 80th anniversary as well as on Bogdan Mielnik and Stanisław Lech Woronowicz on their 75th and 70th birthday, respectively. The groundbreaking work of Berezin is discussed from today’s perspective by presenting an overview of his ideas and their impact on further developments. He was, among other fields, active in representation theory, general concepts of quantization and coherent states, supersymmetry and supermanifolds. Another focus lies on the accomplishments of Bogdan Mielnik and Stanisław Lech Woronowicz. Mielnik’s geometric approach to the description of quantum mixed states, the method of quantum state manipulation and their important implications for quantum computing and quantum entanglement are discussed as well as the intricacies of the quantum time operator. Woronowicz’ fruitful notion of a compact quantum group and related topics are also addressed.