Lie Theory and Its Applications in Physics [electronic resource] : IX International Workshop /
International Workshop on Lie theory and Its Applications in Physics(9th :2011 :Varna, Bulgaria),author.
Dobrev, Vladimir.editor.
Traditionally, Lie Theory is a tool to build mathematical models for physical systems. Recently, the trend is towards geometrisation 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. Geometrisation and symmetries are meant in their broadest sense, i.e., classical geometry, differential geometry, groups and quantum groups, infinite-dimensional (super-)algebras, and their representations. Furthermore, we include the necessary tools from functional analysis and number theory. This is a large interdisciplinary and interrelated field. Samples of these new trends are presented in this volume, based on contributions from the Workshop “Lie Theory and Its Applications in Physics”  held near Varna, Bulgaria, in June 2011. This book is suitable for an extensive audience of mathematicians, mathematical physicists, theoretical physicists, and researchers in the field of Lie Theory.
Description based upon print version of record.
Lie Theory and Its Applications in Physics; Preface; Contents; List of Participants; Part I: Plenary Talks; A Lump Solution in SFT; 1 Introduction; 2 The Analytic Tachyon Vacuum Solution; 3 The Third Conjecture; 3.1 Analytic Lump Solutions; References; Towards p-Adic Matter in the Universe; 1 Introduction; 2 p-Adic Strings; 2.1 p-Adic Numbers and Their Applicability; 2.2 Scattering Amplitudes and Lagrangian for Open Scalar p-Adic Strings; 2.3 New Kind of Matter, Which Has Origin in p-Adic Strings; 3 Adelic Cosmological Modelling; 3.1 Adeles and Their Applicability
3.2 Some Adelic Cosmological Investigations4 Concluding Remarks; References; Palev Statistics and the Chronon; 1 Modular Architecture; 2 Palev Statistics; 2.1 Spins; 2.2 Di-Fermions; 2.3 Regular Space-Times; 2.4 Feynman Space-Time; 2.5 Yang Space-Time-Momentum-Energy; 2.6 Regular Space-Time-Momentum-Energy; 2.7 Interpretation of the Indefinite Norm; 2.8 Locality; 2.9 Quantification and Quantization; 2.10 Gauge; 3 Higher-Order Quantum Set Theory; 3.1 Spin Structure of S""0362S; 3.2 Schur Spinors; 4 Revised Quantum Set Theory; 4.1 Bosons; 4.2 Constituents of the Photon; References
Some Remarks on Weierstrass Sections, Adapted Pairsand Polynomiality1 Introduction; 2 Weierstrass Canonical Form for Elliptic Curves; 3 A Joke and a Misunderstanding; 4 The Hessenberg and Its Generalizations; References; From Palev's Study of Wigner Quantum Systems to New Results on Sums of Schur Functions; 1 Introduction; 2 Preliminaries; 3 Macdonald's Formula; 4 Derivation of the LSV Result; 5 Classical Group Characters; 6 Howe Dual Pairs; 7 Metaplectic Representations; 8 Conclusions; References; Varna Lecture on L2-Analysis of Minimal Representations; 1 What are Minimal Representations?
2 More Symmetric Than Symmetric Spaces3 Schrödinger Model of Minimal Representations; 4 Special Functions to 4th Order Differential Operators; 5 Broken Symmetries and Branching Laws; 6 Generalized Fourier Transform as a Unitary Inversion; 7 SL2-Triple in the Schrödinger Model; 8 Quantization of Kostant-Sekiguchi Correspondence; References; Exponential Series Without Denominators; 1 Introduction; 2 Zinbiel and Dendriform Algebras; 2.1 Definition; 2.2 Free Zinbiel Algebra; 2.4 Example; 2.5 Dendriform Algebra; 2.6 Commutative Dendriform Algebra; 2.8 Dendriform Calculus
2.9 Pre-Lie Product and Brace Products2.10 A Commutative Diagram of Algebras; 3 Exponential Series; 3.1 Exponential Series Without Denominators; 3.4 Zinbiel Algebras in Characteristic p; 4 BCH-Type Formula for the Exponential Series Without Denominators; 4.3 Functional Equation in One Variable; 4.5 The Multilinear Case; References; New Methods in Conformal Partial Wave Analysis; 1 Introduction; 2 Higher Chiral Partial Waves; 3 Intertwining Differential Operators; 4 Application: Test of Positivity of a 6-Point Structure; References
Euclidean Configuration Space Renormalization, Residues and Dilation Anomaly
Includes bibliographical references and index.
Traditionally, Lie Theory is a tool to build mathematical models for physical systems. Recently, the trend is towards geometrisation 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. Geometrisation and symmetries are meant in their broadest sense, i.e., classical geometry, differential geometry, groups and quantum groups, infinite-dimensional (super-)algebras, and their representations. Furthermore, we include the necessary tools from functional analysis and number theory. This is a large interdisciplinary and interrelated field. Samples of these new trends are presented in this volume, based on contributions from the Workshop “Lie Theory and Its Applications in Physics”  held near Varna, Bulgaria, in June 2011. This book is suitable for an extensive audience of mathematicians, mathematical physicists, theoretical physicists, and researchers in the field of Lie Theory.
Algebra.
Topological groups.
Lie groups.
Geometry.
Mathematical physics.
Algebra.
Topological Groups, Lie Groups.
Geometry.
Mathematical Physics.