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The Resource An algebraic geometric approach to separation of variables, Konrad Schöbel
An algebraic geometric approach to separation of variables, Konrad Schöbel
Resource Information
The item An algebraic geometric approach to separation of variables, Konrad Schöbel represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Oklahoma Libraries.This item is available to borrow from all library branches.
Resource Information
The item An algebraic geometric approach to separation of variables, Konrad Schöbel represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Oklahoma Libraries.
This item is available to borrow from all library branches.
 Summary
 Konrad Sch©œbel aims to lay the foundations for a consequent algebraic geometric treatment of variable separation, which is one of the oldest and most powerful methods to construct exact solutions for the fundamental equations in classical and quantum physics. The present work reveals a surprising algebraic geometric structure behind the famous list of separation coordinates, bringing together a great range of mathematics and mathematical physics, from the late 19th century theory of separation of variables to modern moduli space theory, Stasheff polytopes and operads. "I am particularly impressed by his mastery of a variety of techniques and his ability to show clearly how they interact to produce his results.ĺl℗l℗l (Jim Stasheff) ℗l Contents The Foundation: The Algebraic Integrability Conditions The Proof of Concept: A Complete Solution for the 3Sphere The Generalisation: A Solution for Spheres of Arbitrary Dimension The Perspectives: Applications and Generalisations ℗l Target Groups Scientists in the fields of Mathematical Physics and Algebraic Geometry ℗l The Author Konrad Sch©œbel studied physics and mathematics at FriedrichSchiller University Jena (Germany) and Universidad de Granada (Spain) and obtained his PhD at the Universit©♭ de Provence AixMarseille I (France). He now holds a postdoc position at FriedrichSchiller University Jena and works as a research and development engineer for applications in clinical ultrasound diagnostics
 Language
 eng
 Extent
 1 online resource
 Contents

 Preface; Contents; 0 Introduction; 0.1 Separation of variables; 0.2 History; 0.3 Aim; 0.4 Mathematical formulation; 0.4.1 Separation coordinates; 0.4.2 Killing tensors, Nijenhuis integrability and Stäckel systems ; 0.4.3 Observations; 0.4.4 The problems; 0.5 Method; 0.6 Scope; 0.7 Some examples; 0.7.1 Cofactor systems; 0.7.2 Elliptic and polyspherical coordinates; 0.7.3 A trivial and a simple example: Spheres of dimension one and two; 0.8 Overview over the main results; 1 The foundation: the algebraic integrability conditions; 1.1 Young tableaux; 1.2 The 1st integrability condition
 1.3 The 2nd integrability condition1.4 Redundancy of the 3rd integrability condition; 1.5 Commuting Killing tensors; 2 The proof of concept: a complete solution for the 3dimensional sphere; 2.1 Properties of algebraic curvature tensors; 2.1.1 Decomposition; 2.1.2 The action of the isometry group; 2.1.3 Aligned algebraic curvature tensors; 2.1.4 Diagonal algebraic curvature tensors; 2.1.5 The residual action of the isometry group; 2.2 Solution of the algebraic integrability conditions; 2.2.1 Reformulation of the first integrability condition; 2.2.2 Integrability implies diagonalisability
 2.2.3 Solution of the second integrability condition2.3 The algebraic geometry of the KillingStäckel variety ; 2.4 Interpretation of the KillingStäckel variety ; 2.4.1 Stäckel systems and isokernel lines ; 2.4.2 Antisymmetric matrices and special conformal Killing tensors; 2.4.3 Isokernel planes and integrable Killing tensors from S ; 2.5 Separation coordinates; 2.6 The space of separation coordinates; 2.7 The variety of integrable Killing tensors; 3 The generalisation: a solution for spheres of arbitrary dimension; 3.1 An alternative definition of Stäckel systems
 3.2 Killing tensors with diagonal algebraic curvature tensor3.3 The residual action of the isometry group; 3.4 Gaudin subalgebras of the KohnoDrinfeld Lie algebra and the moduli space M0̄,n+1 ; 3.5 The real version M0̄,n+1(R) and Stasheff polytopes ; 3.5.1 Topology; 3.5.2 Combinatorics; 3.5.3 Operad structure; 3.6 The correspondence; 3.7 Applications; 3.7.1 Enumerating separation coordinates; 3.7.2 Constructing separation coordinates via the mosaic operad; 3.7.3 Constructing Stäckel systems via the mosaic operad ; 4 The perspectives: applications and generalisations
 4.1 Other families of Riemannian manifolds4.2 Further notions of variable separation; 4.3 Applications; 4.3.1 Separable potentials.; 4.3.2 Special function theory; 4.3.3 Generalisations of M0̄,n+1(R) ; Acknowledgements; Bibliography
 Isbn
 9783658114084
 Label
 An algebraic geometric approach to separation of variables
 Title
 An algebraic geometric approach to separation of variables
 Statement of responsibility
 Konrad Schöbel
 Language
 eng
 Summary
 Konrad Sch©œbel aims to lay the foundations for a consequent algebraic geometric treatment of variable separation, which is one of the oldest and most powerful methods to construct exact solutions for the fundamental equations in classical and quantum physics. The present work reveals a surprising algebraic geometric structure behind the famous list of separation coordinates, bringing together a great range of mathematics and mathematical physics, from the late 19th century theory of separation of variables to modern moduli space theory, Stasheff polytopes and operads. "I am particularly impressed by his mastery of a variety of techniques and his ability to show clearly how they interact to produce his results.ĺl℗l℗l (Jim Stasheff) ℗l Contents The Foundation: The Algebraic Integrability Conditions The Proof of Concept: A Complete Solution for the 3Sphere The Generalisation: A Solution for Spheres of Arbitrary Dimension The Perspectives: Applications and Generalisations ℗l Target Groups Scientists in the fields of Mathematical Physics and Algebraic Geometry ℗l The Author Konrad Sch©œbel studied physics and mathematics at FriedrichSchiller University Jena (Germany) and Universidad de Granada (Spain) and obtained his PhD at the Universit©♭ de Provence AixMarseille I (France). He now holds a postdoc position at FriedrichSchiller University Jena and works as a research and development engineer for applications in clinical ultrasound diagnostics
 Cataloging source
 N$T
 http://library.link/vocab/creatorName
 Schöbel, Konrad
 Dewey number
 515.353
 Index
 no index present
 LC call number
 QA377
 Literary form
 non fiction
 Nature of contents

 dictionaries
 bibliography
 http://library.link/vocab/subjectName

 Separation of variables
 Differential equations
 MATHEMATICS / Calculus
 MATHEMATICS / Mathematical Analysis
 Differential equations
 Separation of variables
 Label
 An algebraic geometric approach to separation of variables, Konrad Schöbel
 Antecedent source
 unknown
 Bibliography note
 Includes bibliographical references
 Carrier category
 online resource
 Carrier category code

 cr
 Carrier MARC source
 rdacarrier
 Color
 multicolored
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent
 Contents

 Preface; Contents; 0 Introduction; 0.1 Separation of variables; 0.2 History; 0.3 Aim; 0.4 Mathematical formulation; 0.4.1 Separation coordinates; 0.4.2 Killing tensors, Nijenhuis integrability and Stäckel systems ; 0.4.3 Observations; 0.4.4 The problems; 0.5 Method; 0.6 Scope; 0.7 Some examples; 0.7.1 Cofactor systems; 0.7.2 Elliptic and polyspherical coordinates; 0.7.3 A trivial and a simple example: Spheres of dimension one and two; 0.8 Overview over the main results; 1 The foundation: the algebraic integrability conditions; 1.1 Young tableaux; 1.2 The 1st integrability condition
 1.3 The 2nd integrability condition1.4 Redundancy of the 3rd integrability condition; 1.5 Commuting Killing tensors; 2 The proof of concept: a complete solution for the 3dimensional sphere; 2.1 Properties of algebraic curvature tensors; 2.1.1 Decomposition; 2.1.2 The action of the isometry group; 2.1.3 Aligned algebraic curvature tensors; 2.1.4 Diagonal algebraic curvature tensors; 2.1.5 The residual action of the isometry group; 2.2 Solution of the algebraic integrability conditions; 2.2.1 Reformulation of the first integrability condition; 2.2.2 Integrability implies diagonalisability
 2.2.3 Solution of the second integrability condition2.3 The algebraic geometry of the KillingStäckel variety ; 2.4 Interpretation of the KillingStäckel variety ; 2.4.1 Stäckel systems and isokernel lines ; 2.4.2 Antisymmetric matrices and special conformal Killing tensors; 2.4.3 Isokernel planes and integrable Killing tensors from S ; 2.5 Separation coordinates; 2.6 The space of separation coordinates; 2.7 The variety of integrable Killing tensors; 3 The generalisation: a solution for spheres of arbitrary dimension; 3.1 An alternative definition of Stäckel systems
 3.2 Killing tensors with diagonal algebraic curvature tensor3.3 The residual action of the isometry group; 3.4 Gaudin subalgebras of the KohnoDrinfeld Lie algebra and the moduli space M0̄,n+1 ; 3.5 The real version M0̄,n+1(R) and Stasheff polytopes ; 3.5.1 Topology; 3.5.2 Combinatorics; 3.5.3 Operad structure; 3.6 The correspondence; 3.7 Applications; 3.7.1 Enumerating separation coordinates; 3.7.2 Constructing separation coordinates via the mosaic operad; 3.7.3 Constructing Stäckel systems via the mosaic operad ; 4 The perspectives: applications and generalisations
 4.1 Other families of Riemannian manifolds4.2 Further notions of variable separation; 4.3 Applications; 4.3.1 Separable potentials.; 4.3.2 Special function theory; 4.3.3 Generalisations of M0̄,n+1(R) ; Acknowledgements; Bibliography
 Dimensions
 unknown
 Extent
 1 online resource
 File format
 unknown
 Form of item
 online
 Isbn
 9783658114084
 Level of compression
 unknown
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code

 c
 Note
 SpringerLink
 Other control number
 10.1007/9783658114084
 Quality assurance targets
 not applicable
 Reformatting quality
 unknown
 Sound
 unknown sound
 Specific material designation
 remote
 System control number

 (OCoLC)925478417
 (OCoLC)ocn925478417
 Label
 An algebraic geometric approach to separation of variables, Konrad Schöbel
 Antecedent source
 unknown
 Bibliography note
 Includes bibliographical references
 Carrier category
 online resource
 Carrier category code

 cr
 Carrier MARC source
 rdacarrier
 Color
 multicolored
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent
 Contents

 Preface; Contents; 0 Introduction; 0.1 Separation of variables; 0.2 History; 0.3 Aim; 0.4 Mathematical formulation; 0.4.1 Separation coordinates; 0.4.2 Killing tensors, Nijenhuis integrability and Stäckel systems ; 0.4.3 Observations; 0.4.4 The problems; 0.5 Method; 0.6 Scope; 0.7 Some examples; 0.7.1 Cofactor systems; 0.7.2 Elliptic and polyspherical coordinates; 0.7.3 A trivial and a simple example: Spheres of dimension one and two; 0.8 Overview over the main results; 1 The foundation: the algebraic integrability conditions; 1.1 Young tableaux; 1.2 The 1st integrability condition
 1.3 The 2nd integrability condition1.4 Redundancy of the 3rd integrability condition; 1.5 Commuting Killing tensors; 2 The proof of concept: a complete solution for the 3dimensional sphere; 2.1 Properties of algebraic curvature tensors; 2.1.1 Decomposition; 2.1.2 The action of the isometry group; 2.1.3 Aligned algebraic curvature tensors; 2.1.4 Diagonal algebraic curvature tensors; 2.1.5 The residual action of the isometry group; 2.2 Solution of the algebraic integrability conditions; 2.2.1 Reformulation of the first integrability condition; 2.2.2 Integrability implies diagonalisability
 2.2.3 Solution of the second integrability condition2.3 The algebraic geometry of the KillingStäckel variety ; 2.4 Interpretation of the KillingStäckel variety ; 2.4.1 Stäckel systems and isokernel lines ; 2.4.2 Antisymmetric matrices and special conformal Killing tensors; 2.4.3 Isokernel planes and integrable Killing tensors from S ; 2.5 Separation coordinates; 2.6 The space of separation coordinates; 2.7 The variety of integrable Killing tensors; 3 The generalisation: a solution for spheres of arbitrary dimension; 3.1 An alternative definition of Stäckel systems
 3.2 Killing tensors with diagonal algebraic curvature tensor3.3 The residual action of the isometry group; 3.4 Gaudin subalgebras of the KohnoDrinfeld Lie algebra and the moduli space M0̄,n+1 ; 3.5 The real version M0̄,n+1(R) and Stasheff polytopes ; 3.5.1 Topology; 3.5.2 Combinatorics; 3.5.3 Operad structure; 3.6 The correspondence; 3.7 Applications; 3.7.1 Enumerating separation coordinates; 3.7.2 Constructing separation coordinates via the mosaic operad; 3.7.3 Constructing Stäckel systems via the mosaic operad ; 4 The perspectives: applications and generalisations
 4.1 Other families of Riemannian manifolds4.2 Further notions of variable separation; 4.3 Applications; 4.3.1 Separable potentials.; 4.3.2 Special function theory; 4.3.3 Generalisations of M0̄,n+1(R) ; Acknowledgements; Bibliography
 Dimensions
 unknown
 Extent
 1 online resource
 File format
 unknown
 Form of item
 online
 Isbn
 9783658114084
 Level of compression
 unknown
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code

 c
 Note
 SpringerLink
 Other control number
 10.1007/9783658114084
 Quality assurance targets
 not applicable
 Reformatting quality
 unknown
 Sound
 unknown sound
 Specific material designation
 remote
 System control number

 (OCoLC)925478417
 (OCoLC)ocn925478417
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