Groups, Systems and Many-Body Physics

by Peter Dal Cin

Overview

The authors of the present book share the view that groups and semigroups playa fundamental role in the structure of the complex systems which they are studying. A serious effort was made to implement this point of view by presenting the fundamental concepts pertaining to groups and semigroups before going into the various fields of application. The first two chapters are written in this spirit. The following seven chapters deal with groups in relation to specific systems and lead from basic notions to high-level applications. The systems under study are in all cases characterized by a high degree of complexity as found in the physics of many degrees of freedom and in the theory of automata and systems. In 1977 the authors from the University of Tiibingen (M. Dal Cin, G. John, P. Kramer, A. Rieckers, K. Scheerer and H. Stumpf) organized an International Summer School on Groups and Many-Body Physics. The lectures presented at this School dealt specifically with this interplay of groups and complex systems. The contributions of this book cover the fields which were treated in a condensed form at the Summer School.

Product Details

ISBN-13:	9783528084448
Publisher:	Vieweg+Teubner Verlag
Publication date:	01/01/1980
Series:	Vieweg tracts in pure and applied physics , #4
Edition description:	Softcover reprint of the original 1st ed. 1980
Pages:	412
Product dimensions:	6.69(w) x 9.61(h) x 0.03(d)

Table of Contents

I Fundamentals on Semigroups, Groups and Representations.- 1 Groups and group action.- 2 Examples of groups.- 3 Subgroup structures of groups and semigroups.- 4 Groups and topology.- 5 Representations of groups.- 6 Induced representations of the Poincaré group.- References.- II Fundamentals of Algebraic Quantum Theory.- Appendix: Jordan homomorphisms.- References.- III Pauli Principle and Indirect Exchange Phenomena in Molecules and Solids.- 1 Permutation symmetry and chemical bonding in molecules and solids.- References.- 2 Group-theoretical aspects pertaining to the quantum-mechanical N-particle system.- 3 The effective electron model: Applications.- References.- IV Groups and Semigroups for Composite Nucleon Systems.- 1 Introduction.- 2 Exchange and double cosets of the symmetric group.- 3 Orbital symmetry and the representation of the symmetric and general linear groups.- 4 Weyl operators, linear canonical transformations and Bargmann Hilbert space.- 5 Canonical transformations forinteracting n-body systems.- 6 Interaction of composite particles.- 7 Configurations of simple composite particles.- 8 Composite particles with a closed-shell configuration.- 9 Conclusion.- References.- V An Algebraic Approach for Spontaneous Symmetry Breaking in Quantum Statistical Mechanics.- 1 Introduction.- 2 General theory.- 3 Exactly solvable models.- 4 Existence of crystals.- References.- VI Dynamical Groups for the Motion of Relativistic Composite Systems.- 1 Introduction.- 2 The general framework.- 3 Composite systems and reducible representations.- 4 The method of induced representations from dynamical groups.- 5 Electron-positron complex.- 6 Composite systems. Inductive approach.- 7 Dynamical algebras, their contraction and generalizations.- 8 Passage to relativistic wave equations.- 9 Principles on the choice of infinite component wave equations.- 10 The Majorana “particle”.- 11 An inverse problem.- 12 The class of composite systems based on conformal group.- 13 Electromagnetric interactions of composite systems.- 14 Other interactions of composite systems.- 15 A characteristic property of relativistic composite systems: Space-like states.- References.- VII New Representation Spaces of the Poincaré Group and Functional Quantum Theory.- References.- VIII The Algebraic Theory of Automata.- References.- IX On the (Internal) Symmetry Groups of Linear Dynamical Systems.- 1 Introduction and statement of the main definitions and results.- 2 Complete Teachability and complete observability.- 3 Nice selections and the local structure of Lm,n,pcr/GLn(IR).- 4 Realization theory.- 5 Feedback splits the external description degeneracy.- 6 Description of Lm,n,pco,cr(IR)/GLn(IR). Invariants.- 7 On the (non-)existence of canonical forms.- 8 On the geometry of Mm,n,pco,cr(IR). Holes and (partial) compactifications.- References.