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In the last decade, the development of new ideas in quantum theory, including geometric and deformation quantization, the non-Abelian Berry's geometric factor, super- and BRST symmetries, non-commutativity, has called into play the geometric techniques based on the deep interplay between algebra, differential geometry and topology. The book aims at being a guide to advanced differential geometric and topological methods in quantum mechanics. Their main peculiarity lies in the fact that geometry in quantum theory speaks mainly the algebraic language of rings, modules, sheaves and categories. Ge

Quantum theory. --- Geometric quantization. --- Topology. --- Mathematical physics. --- Physical mathematics --- Physics --- Analysis situs --- Position analysis --- Rubber-sheet geometry --- Geometry --- Polyhedra --- Set theory --- Algebras, Linear --- Geometry, Quantum --- Quantization, Geometric --- Quantum geometry --- Geometry, Differential --- Quantum theory --- Quantum dynamics --- Quantum mechanics --- Quantum physics --- Mechanics --- Thermodynamics --- Mathematics

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The geometric formulation of autonomous Hamiltonian mechanics in the terms of symplectic and Poisson manifolds is generally accepted. The literature on this subject is extensive. The present book provides the geometric formulation of non-autonomous mechanics in a general setting of time-dependent coordinate and reference frame transformations. This formulation of mechanics as like as that of classical field theory lies in the framework of general theory of dynamic systems, and Lagrangian and Hamiltonian formalisms on fiber bundles. The reader will find a strict mathematical exposition of non-a

Statistical mechanics. --- Quantum theory --- Geometry, Differential. --- Mathematical physics. --- Mathematics.