Conformal Symmetry Breaking Operators For Differential Forms On Spheres

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Conformal Symmetry Breaking Operators for Differential Forms on Spheres

Author : Toshiyuki Kobayashi
Publisher : Springer
ISBN 13 : 9811026572
Total Pages : 191 pages
Book Rating : 4.8/5 (11 download)

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Book Synopsis Conformal Symmetry Breaking Operators for Differential Forms on Spheres by : Toshiyuki Kobayashi

Download or read book Conformal Symmetry Breaking Operators for Differential Forms on Spheres written by Toshiyuki Kobayashi and published by Springer. This book was released on 2016-10-11 with total page 191 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work is the first systematic study of all possible conformally covariant differential operators transforming differential forms on a Riemannian manifold X into those on a submanifold Y with focus on the model space (X, Y) = (Sn, Sn-1). The authors give a complete classification of all such conformally covariant differential operators, and find their explicit formulæ in the flat coordinates in terms of basic operators in differential geometry and classical hypergeometric polynomials. Resulting families of operators are natural generalizations of the Rankin–Cohen brackets for modular forms and Juhl's operators from conformal holography. The matrix-valued factorization identities among all possible combinations of conformally covariant differential operators are also established. The main machinery of the proof relies on the "F-method" recently introduced and developed by the authors. It is a general method to construct intertwining operators between C∞-induced representations or to find singular vectors of Verma modules in the context of branching rules, as solutions to differential equations on the Fourier transform side. The book gives a new extension of the F-method to the matrix-valued case in the general setting, which could be applied to other problems as well. This book offers a self-contained introduction to the analysis of symmetry breaking operators for infinite-dimensional representations of reductive Lie groups. This feature will be helpful for active scientists and accessible to graduate students and young researchers in differential geometry, representation theory, and theoretical physics.

Conformal Symmetry Breaking Differential Operators on Differential Forms

Author : Matthias Fischmann
Publisher : American Mathematical Soc.
ISBN 13 : 1470443244
Total Pages : 112 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Conformal Symmetry Breaking Differential Operators on Differential Forms by : Matthias Fischmann

Download or read book Conformal Symmetry Breaking Differential Operators on Differential Forms written by Matthias Fischmann and published by American Mathematical Soc.. This book was released on 2021-06-18 with total page 112 pages. Available in PDF, EPUB and Kindle. Book excerpt: We study conformal symmetry breaking diﬀerential operators which map dif-ferential forms on Rn to diﬀerential forms on a codimension one subspace Rn−1. These operators are equivariant with respect to the conformal Lie algebra of the subspace Rn−1. They correspond to homomorphisms of generalized Verma mod-ules for so(n, 1) into generalized Verma modules for so(n+1, 1) both being induced from fundamental form representations of a parabolic subalgebra. We apply the F -method to derive explicit formulas for such homomorphisms. In particular, we ﬁnd explicit formulas for the generators of the intertwining operators of the re-lated branching problems restricting generalized Verma modules for so(n +1, 1) to so(n, 1). As consequences, we derive closed formulas for all conformal symmetry breaking diﬀerential operators in terms of the ﬁrst-order operators d, δ, d¯ and δ¯ and certain hypergeometric polynomials. A dominant role in these studies is played by two inﬁnite sequences of symmetry breaking diﬀerential operators which depend on a complex parameter λ. Their values at special values of λ appear as factors in two systems of factorization identities which involve the Branson-Gover opera- tors of the Euclidean metrics on Rn and Rn−1 and the operators d, δ, d¯ and δ¯ as factors, respectively. Moreover, they naturally recover the gauge companion and Q-curvature operators of the Euclidean metric on the subspace Rn−1, respectively.

Geometric Methods in Physics XXXV

Author : Piotr Kielanowski
Publisher : Birkhäuser
ISBN 13 : 3319635948
Total Pages : 280 pages
Book Rating : 4.3/5 (196 download)

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Book Synopsis Geometric Methods in Physics XXXV by : Piotr Kielanowski

Download or read book Geometric Methods in Physics XXXV written by Piotr Kielanowski and published by Birkhäuser. This book was released on 2018-02-10 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book features a selection of articles based on the XXXV Białowieża Workshop on Geometric Methods in Physics, 2016. The series of Białowieża workshops, attended by a community of experts at the crossroads of mathematics and physics, is a major annual event in the field. The works in this book, based on presentations given at the workshop, are previously unpublished, at the cutting edge of current research, typically grounded in geometry and analysis, and with applications to classical and quantum physics. In 2016 the special session "Integrability and Geometry" in particular attracted pioneers and leading specialists in the field. Traditionally, the Białowieża Workshop is followed by a School on Geometry and Physics, for advanced graduate students and early-career researchers, and the book also includes extended abstracts of the lecture series.

Quantum Theory and Symmetries with Lie Theory and Its Applications in Physics Volume 1

Author : Vladimir Dobrev
Publisher : Springer
ISBN 13 : 9811327157
Total Pages : 419 pages
Book Rating : 4.8/5 (113 download)

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Book Synopsis Quantum Theory and Symmetries with Lie Theory and Its Applications in Physics Volume 1 by : Vladimir Dobrev

Download or read book Quantum Theory and Symmetries with Lie Theory and Its Applications in Physics Volume 1 written by Vladimir Dobrev and published by Springer. This book was released on 2018-11-28 with total page 419 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the first volume of proceedings from the joint conference X International Symposium “Quantum Theory and Symmetries” (QTS-X) and XII International Workshop “Lie Theory and Its Applications in Physics” (LT-XII), held on 19–25 June 2017 in Varna, Bulgaria. The QTS series was founded on the core principle that symmetries underlie all descriptions of quantum systems. It has since evolved into a symposium at the forefront of theoretical and mathematical physics. The LT series covers the whole field of Lie theory in its widest sense, together with its applications in many areas of physics. As an interface between mathematics and physics, the workshop serves as a meeting place for mathematicians and theoretical and mathematical physicists. In dividing the material between the two volumes, the Editor has sought to select papers that are more oriented toward mathematics for the first volume, and those focusing more on physics for the second. However, this division is relative, since many papers are equally suitable for either volume. The topics addressed in this volume represent the latest trends in the fields covered by the joint conferences: representation theory, integrability, entanglement, quantum groups, number theory, conformal geometry, quantum affine superalgebras, noncommutative geometry. Further, they present various mathematical results: on minuscule modules, symmetry breaking operators, Kashiwara crystals, meta-conformal invariance, the superintegrable Zernike system.

Lie Theory and Its Applications in Physics

Author : Vladimir Dobrev
Publisher : Springer Nature
ISBN 13 : 9811577757
Total Pages : 545 pages
Book Rating : 4.8/5 (115 download)

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Book Synopsis Lie Theory and Its Applications in Physics by : Vladimir Dobrev

Download or read book Lie Theory and Its Applications in Physics written by Vladimir Dobrev and published by Springer Nature. This book was released on 2020-10-15 with total page 545 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents modern trends in the area of symmetries and their applications based on contributions to the workshop "Lie Theory and Its Applications in Physics" held near Varna (Bulgaria) in June 2019. Traditionally, Lie theory is a tool to build mathematical models for physical systems. Recently, the trend is towards geometrization of the mathematical description of physical systems and objects. A geometric approach to a system yields in general some notion of symmetry, which is very helpful in understanding its structure. Geometrization and symmetries are meant in their widest sense, i.e., representation theory, algebraic geometry, number theory, infinite-dimensional Lie algebras and groups, superalgebras and supergroups, groups and quantum groups, noncommutative geometry, symmetries of linear and nonlinear partial differential operators, special functions, and others. Furthermore, the necessary tools from functional analysis are included. This is a large interdisciplinary and interrelated field. The topics covered in this volume from the workshop represent the most modern trends in the field : Representation Theory, Symmetries in String Theories, Symmetries in Gravity Theories, Supergravity, Conformal Field Theory, Integrable Systems, Polylogarithms, and Supersymmetry. They also include Supersymmetric Calogero-type models, Quantum Groups, Deformations, Quantum Computing and Deep Learning, Entanglement, Applications to Quantum Theory, and Exceptional Quantum Algebra for the standard model of particle physics This book is suitable for a broad audience of mathematicians, mathematical physicists, and theoretical physicists, including researchers and graduate students interested in Lie Theory.

Symmetry Breaking for Representations of Rank One Orthogonal Groups II

Author : Toshiyuki Kobayashi
Publisher : Springer
ISBN 13 : 981132901X
Total Pages : 350 pages
Book Rating : 4.8/5 (113 download)

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Book Synopsis Symmetry Breaking for Representations of Rank One Orthogonal Groups II by : Toshiyuki Kobayashi

Download or read book Symmetry Breaking for Representations of Rank One Orthogonal Groups II written by Toshiyuki Kobayashi and published by Springer. This book was released on 2018-12-27 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work provides the first classification theory of matrix-valued symmetry breaking operators from principal series representations of a reductive group to those of its subgroup.The study of symmetry breaking operators (intertwining operators for restriction) is an important and very active research area in modern representation theory, which also interacts with various fields in mathematics and theoretical physics ranging from number theory to differential geometry and quantum mechanics.The first author initiated a program of the general study of symmetry breaking operators. The present book pursues the program by introducing new ideas and techniques, giving a systematic and detailed treatment in the case of orthogonal groups of real rank one, which will serve as models for further research in other settings.In connection to automorphic forms, this work includes a proof for a multiplicity conjecture by Gross and Prasad for tempered principal series representations in the case (SO(n + 1, 1), SO(n, 1)). The authors propose a further multiplicity conjecture for nontempered representations.Viewed from differential geometry, this seminal work accomplishes the classification of all conformally covariant operators transforming differential forms on a Riemanniann manifold X to those on a submanifold in the model space (X, Y) = (Sn, Sn-1). Functional equations and explicit formulæ of these operators are also established.This book offers a self-contained and inspiring introduction to the analysis of symmetry breaking operators for infinite-dimensional representations of reductive Lie groups. This feature will be helpful for active scientists and accessible to graduate students and young researchers in representation theory, automorphic forms, differential geometry, and theoretical physics.

Representation Theory and Harmonic Analysis on Symmetric Spaces

Author : Jens Gerlach Christensen
Publisher : American Mathematical Soc.
ISBN 13 : 1470440709
Total Pages : 330 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Representation Theory and Harmonic Analysis on Symmetric Spaces by : Jens Gerlach Christensen

Download or read book Representation Theory and Harmonic Analysis on Symmetric Spaces written by Jens Gerlach Christensen and published by American Mathematical Soc.. This book was released on 2018-08-27 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the AMS Special Session on Harmonic Analysis, in honor of Gestur Ólafsson's 65th birthday, held on January 4, 2017, in Atlanta, Georgia. The articles in this volume provide fresh perspectives on many different directions within harmonic analysis, highlighting the connections between harmonic analysis and the areas of integral geometry, complex analysis, operator algebras, Lie algebras, special functions, and differential operators. The breadth of contributions highlights the diversity of current research in harmonic analysis and shows that it continues to be a vibrant and fruitful field of inquiry.

Introduction to Möbius Differential Geometry

Author : Udo Hertrich-Jeromin
Publisher : Cambridge University Press
ISBN 13 : 9780521535694
Total Pages : 436 pages
Book Rating : 4.5/5 (356 download)

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Book Synopsis Introduction to Möbius Differential Geometry by : Udo Hertrich-Jeromin

Download or read book Introduction to Möbius Differential Geometry written by Udo Hertrich-Jeromin and published by Cambridge University Press. This book was released on 2003-08-14 with total page 436 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces the reader to the geometry of surfaces and submanifolds in the conformal n-sphere.

Mathematical Reviews

Author :
Publisher :
ISBN 13 :
Total Pages : 764 pages
Book Rating : 4.X/5 (6 download)

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Book Synopsis Mathematical Reviews by :

Download or read book Mathematical Reviews written by and published by . This book was released on 2001 with total page 764 pages. Available in PDF, EPUB and Kindle. Book excerpt:

The Laplacian on a Riemannian Manifold

Author : Steven Rosenberg
Publisher : Cambridge University Press
ISBN 13 : 9780521468312
Total Pages : 190 pages
Book Rating : 4.4/5 (683 download)

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Book Synopsis The Laplacian on a Riemannian Manifold by : Steven Rosenberg

Download or read book The Laplacian on a Riemannian Manifold written by Steven Rosenberg and published by Cambridge University Press. This book was released on 1997-01-09 with total page 190 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text on analysis of Riemannian manifolds is aimed at students who have had a first course in differentiable manifolds.

Diagonalizing Quadratic Bosonic Operators by Non-Autonomous Flow Equations

Author : Volker Bach
Publisher : American Mathematical Soc.
ISBN 13 : 1470417057
Total Pages : 134 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Diagonalizing Quadratic Bosonic Operators by Non-Autonomous Flow Equations by : Volker Bach

Download or read book Diagonalizing Quadratic Bosonic Operators by Non-Autonomous Flow Equations written by Volker Bach and published by American Mathematical Soc.. This book was released on 2016-03-10 with total page 134 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors study a non-autonomous, non-linear evolution equation on the space of operators on a complex Hilbert space. They specify assumptions that ensure the global existence of its solutions and allow them to derive its asymptotics at temporal infinity. They demonstrate that these assumptions are optimal in a suitable sense and more general than those used before. The evolution equation derives from the Brocket-Wegner flow that was proposed to diagonalize matrices and operators by a strongly continuous unitary flow. In fact, the solution of the non-linear flow equation leads to a diagonalization of Hamiltonian operators in boson quantum field theory which are quadratic in the field.

A Complete Creation Field Theory Model Based on Symmetry Breaking of the Homogeneous 5D Space-Time Universe with Primordial Magnetic Monopole Frequencies

Download A Complete Creation Field Theory Model Based on Symmetry Breaking of the Homogeneous 5D Space-Time Universe with Primordial Magnetic Monopole Frequencies PDF Online Free

Author : Wan Ki CHOW
Publisher : Scientific Research Publishing, Inc. USA
ISBN 13 : 1649973047
Total Pages : 359 pages
Book Rating : 4.6/5 (499 download)

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Book Synopsis A Complete Creation Field Theory Model Based on Symmetry Breaking of the Homogeneous 5D Space-Time Universe with Primordial Magnetic Monopole Frequencies by : Wan Ki CHOW

Download or read book A Complete Creation Field Theory Model Based on Symmetry Breaking of the Homogeneous 5D Space-Time Universe with Primordial Magnetic Monopole Frequencies written by Wan Ki CHOW and published by Scientific Research Publishing, Inc. USA. This book was released on 2022-06-20 with total page 359 pages. Available in PDF, EPUB and Kindle. Book excerpt: A book titled “The Five Dimension Space-Time Universe: A creation and grand unified field theory model” was published by Scientific Research Publishing, USA in 2014. Since then, two more friends, Professors Fung and Chow joined the effort. Many more articles with rigorous mathematical foundation extensions were published, including solving for the first time the explicit form of the Maxwell’s magnetic monopoles. It is then clear why there must be a Bose-Einstein vacuum as suggested by Higgs, and all matters can be considered as thermal excitations from it. In fact, the theory works extremely well from astronomical objects, like stars and planets to the precise calculated mass for the proton and neutron, leading to revelation of a precise quark mass of 33 MeV. A first implication that a General Musical Code might exist in the 5D homogenous space-time manifold. Perhaps the most insightful is that the 4th space dimension within the 5D homogenous manifold is actually an entangled variable to the Fermat’s amplitude ‘r’, according to Euler Theorem on 5D manifold. One important consequence is that in the Fourier energy and momentum representation, the 4th momentum variable is completely imaginary. Such a result leads to the emergence of the Higgs bosons, with a primordial spectrum. Based on the crucial steps of deduction briefly outlined above, the current book is written.

Symmetry Breaking for Representations of Rank One Orthogonal Groups

Author : Toshiyuki Kobayashi
Publisher : American Mathematical Soc.
ISBN 13 : 147041922X
Total Pages : 124 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Symmetry Breaking for Representations of Rank One Orthogonal Groups by : Toshiyuki Kobayashi

Download or read book Symmetry Breaking for Representations of Rank One Orthogonal Groups written by Toshiyuki Kobayashi and published by American Mathematical Soc.. This book was released on 2015-10-27 with total page 124 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors give a complete classification of intertwining operators (symmetry breaking operators) between spherical principal series representations of and . They construct three meromorphic families of the symmetry breaking operators, and find their distribution kernels and their residues at all poles explicitly. Symmetry breaking operators at exceptional discrete parameters are thoroughly studied. The authors obtain closed formulae for the functional equations which the composition of the symmetry breaking operators with the Knapp-Stein intertwining operators of and satisfy, and use them to determine the symmetry breaking operators between irreducible composition factors of the spherical principal series representations of and . Some applications are included.

Physics Briefs

Author :
Publisher :
ISBN 13 :
Total Pages : 916 pages
Book Rating : 4.3/5 (91 download)

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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 916 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Encyclopaedia of Mathematics

Author : Michiel Hazewinkel
Publisher : Springer Science & Business Media
ISBN 13 : 9401512795
Total Pages : 639 pages
Book Rating : 4.4/5 (15 download)

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Book Synopsis Encyclopaedia of Mathematics by : Michiel Hazewinkel

Download or read book Encyclopaedia of Mathematics written by Michiel Hazewinkel and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 639 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the second supplementary volume to Kluwer's highly acclaimed eleven-volume Encyclopaedia of Mathematics. This additional volume contains nearly 500 new entries written by experts and covers developments and topics not included in the previous volumes. These entries are arranged alphabetically throughout and a detailed index is included. This supplementary volume enhances the existing eleven volumes, and together these twelve volumes represent the most authoritative, comprehensive and up-to-date Encyclopaedia of Mathematics available.

Exotic Smoothness And Physics: Differential Topology And Spacetime Models

Author : Torsten Asselmeyer-maluga
Publisher : World Scientific
ISBN 13 : 9814493740
Total Pages : 339 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Exotic Smoothness And Physics: Differential Topology And Spacetime Models by : Torsten Asselmeyer-maluga

Download or read book Exotic Smoothness And Physics: Differential Topology And Spacetime Models written by Torsten Asselmeyer-maluga and published by World Scientific. This book was released on 2007-01-23 with total page 339 pages. Available in PDF, EPUB and Kindle. Book excerpt: The recent revolution in differential topology related to the discovery of non-standard (”exotic”) smoothness structures on topologically trivial manifolds such as R4 suggests many exciting opportunities for applications of potentially deep importance for the spacetime models of theoretical physics, especially general relativity. This rich panoply of new differentiable structures lies in the previously unexplored region between topology and geometry. Just as physical geometry was thought to be trivial before Einstein, physicists have continued to work under the tacit — but now shown to be incorrect — assumption that differentiability is uniquely determined by topology for simple four-manifolds. Since diffeomorphisms are the mathematical models for physical coordinate transformations, Einstein's relativity principle requires that these models be physically inequivalent. This book provides an introductory survey of some of the relevant mathematics and presents preliminary results and suggestions for further applications to spacetime models.

Noncommutative Geometry

Author : Alain Connes
Publisher : Springer
ISBN 13 : 3540397027
Total Pages : 364 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Noncommutative Geometry by : Alain Connes

Download or read book Noncommutative Geometry written by Alain Connes and published by Springer. This book was released on 2003-12-15 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt: Noncommutative Geometry is one of the most deep and vital research subjects of present-day Mathematics. Its development, mainly due to Alain Connes, is providing an increasing number of applications and deeper insights for instance in Foliations, K-Theory, Index Theory, Number Theory but also in Quantum Physics of elementary particles. The purpose of the Summer School in Martina Franca was to offer a fresh invitation to the subject and closely related topics; the contributions in this volume include the four main lectures, cover advanced developments and are delivered by prominent specialists.