Momentum Maps and Hamiltonian Reduction

Erscheinungsjahr 2013
ISBN: 978-1-4757-3813-1
Verlag: Birkhäuser

Buch, Englisch, 501 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 803 g

Reihe: Progress in Mathematics

The use of symmetries and conservation laws in the qualitative description of dynamics has a long history going back to the founders of classical mechanics. The focus of this work is a comprehensive and self-contained presentation of the intimate connection between symmetries, conservation laws, and reduction, treating the singular case in detail. This Ferran Sunyer i Balaguer Prize-winning monograph is the first self-contained and thorough presentation of the theory of Hamiltonian reduction in the presence of singularities. It can serve as a resource for graduate courses and seminars in symplectic and Poisson geometry, mechanics, Lie theory, mathematical physics, and as a comprehensive reference resource for researchers.

Zielgruppe

Research

Autoren/Hrsg.

Ortega, Juan-Pablo

Ratiu, Tudor S.

Fachgebiete

• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik
• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Mathematik | Informatik Mathematik Algebra Algebraische Strukturen, Gruppentheorie

Inhaltsverzeichnis

1 Manifolds and Smooth Structures.- 2 Lie Group Actions.- 3 Pseudogroups and Groupoids.- 4 The Standard Momentum Map.- 5 Generalizations of the Momentum Map.- 6 Regular Symplectic Reduction Theory.- 7 The Symplectic Slice Theorem.- 8 Singular Reduction and the Stratification Theorem.- 9 Optimal Reduction.- 10 Poisson Reduction.- 11 Dual Pairs.