Groups, Systems and Many-Body Physics

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Vieweg tracts in pure and applied physics 4

ISBN:	3528084448
ISBN 13:	9783528084448
Autor:	Dal Cin, Peter
Verlag:	Springer Vieweg
Umfang:	xvi, 412 S., 67 s/w Illustr.
Erscheinungsdatum:	01.01.1980
Auflage:	1/1980
Produktform:	Kartoniert
Einband:	Kartoniert

InhaltsangabeI Fundamentals on Semigroups, Groups and Representations.- 1 Groups and group action.- 1.1 Preliminaries.- 1.2 Algebraic composition, semigroups and groups.- 1.3 Transformation groups.- 2 Examples of groups.- 2.1 The symmetric group S(n).- 2.2 Matrix semi-groups and inner products.- 2.3 Inhomogeneous matrix groups.- 3 Subgroup structures of groups and semigroups.- 3.1 Preliminaries: complexes and lattices.- 3.2 Subgroup diagrams.- 3.3 Morphisms and subgroups.- 3.4 Direct and semidirect products.- 3.5 Subnormal chains.- 3.6 Subgroups of semigroups.- 4 Groups and topology.- 4.1 Topological groups.- 4.2 Lie groups.- 4.3 Invariant measures.- 5 Representations of groups.- 5.1 General properties of representations.- 5.2 Irreducible representations of the symmetric group.- 5.3 Finite irreducible representations of the general linear group.- 5.4 Group algebras and representations.- 5.5 Induced and subduced representations.- 6 Induced representations of the Poincaré group.- 6.1 Poincaré transformations.- 6.2 Representations.- 6.3 Induced representations.- 6.4 UIR’s of the Poincaré group.- 6.5 The Dirac equation.- References.- II Fundamentals of Algebraic Quantum Theory.- 1 Algebra of observables.- 2 States.- 3 Symmetry transformations.- 4 Represented systems and symmetries.- 5 Dynamical symmetries and equilibrium states.- 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.- 1.1 Permutation symmetry and exchange interactions.- 1.2 Exchange interactions and chemical bonding.- 1.3 The Heisenberg (effective spin-) Hamiltonian approach to exchange interactions.- References.- 2 Group-theoretical aspects pertaining to the quantum-mechanical N-particle system.- 2.1 Introduction.- 2.1.1 Hamilton operator and Hilbert space.- 2.1.2 Symmetry and Wigner’s theorem. The irreducibility postulate, the identity postulate and the Pauli postulate.- 2.1.3 The spin free Pauli principle.- Appendix A The Schur-Weyl theorem.- Electrbn spin and permutation symmetry.- 2.2 Symmetry adaptation.- 2.2.1 Matric bases.- 2.2.2 Some fundamental expressions pertaining to matric bases.- 2.2.3 Some special choices of matric bases, G = SN.- 2.2.4 Symmetry adaptation of Vn ?N to SN.- 2.2.5 Antisymmetrization.- Appendix B Sequence adaption. Double coset decomposition of unitary matric bases.- Appendix C Tableau operators.- Invariance groups for tableaux operators.- 2.3 Matrix elements and their evaluation.- 2.3.1 Introduction.- 2.3.2 Matrix elements over Young-Yamanouchi N-electron spin (S, M) eigenfunctions.- 2.3.3 Matrix elements of a spin-free observable over sequence-symmetryadapted bases.- 2.3.4 Matrix elements of the spin-free N-electron Hamilton operator over Young unil-type Y?-projected N-electron bases. Pauling numbers.- 2.3.5 Summary and Discussion.- Appendix D The triple double coset symbol, double cosets, DC.- References.- Appendix E The canonical double coset symbol.- References.- Appendix F General references.- Appendix G Special references.- 3 The effective electron model: Applications.- 3.1 Introduction.- 3.2 Effective-electron model for weak chemical bonding.- 3.3 Applications of the model.- 3.3.1 Indirect exchange interactions in magnetic solids.- 3.3.2 Stability of rare-gas halides: A case of selective valence.- 3.3.3 Rotational barriers in simple molecules.- 3.3.4 Magnetic structures of the manganese pyrites.- 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 for interacting n-body systems.- 6 Interaction of composite particles.- 7 Configurations of simple composite particles.- 8 Composite particles with a closed-shell configuration.- 9

Artikelnummer: 5968448 Kategorie: Allgemeines, Lexika

Beschreibung

Beschreibung

The authors of the present book share the view that groups and semigroups playa funda mental 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.