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Topological groups. Lie groups

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This monograph provides an account of the structure of gauge theories from a group theoretical point of view. The first part of the text is devoted to a review of those aspects of compact Lie groups (the Lie algebras, the representation theory, and the global structure) which are necessary for the application of group theory to the physics of particles and fields. The second part describes the way in which compact Lie groups are used to construct gauge theories. Models that describe the known fundamental interactions and the proposed unification of these interactions (grand unified theories) are considered in some detail. The book concludes with an up to date description of the group structure of spontaneous symmetry breakdown, which plays a vital role in these interactions. This book will be of interest to graduate students and to researchers in theoretical physics and applied mathematics, especially those interested in the applications of differential geometry and group theory in physics.

Gauge fields (Physics) --- Broken symmetry (Physics) --- Lie groups.

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Topological groups. Lie groups --- Ordered algebraic structures --- Lie algebras --- Lie groups --- 512.81 --- Groups, Lie --- Symmetric spaces --- Topological groups --- Algebras, Lie --- Algebra, Abstract --- Algebras, Linear --- Lie algebras. --- Lie groups. --- 512.81 Lie groups --- Lie, Algèbres de --- Lie, Groupes de --- Lie, Algèbres de --- Application des groupes a la physique

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This monograph treats an extensively developed field in modern mathematical physics - the theory of generalized coherent states and their applications to various physical problems. Coherent states, introduced originally by Schrodinger and von Neumann, were later employed by Glauber for a quantal description of laser light beams. The concept was generalized by the author for an arbitrary Lie group. In the last decade the formalism has been widely applied to various domains of theoretical physics and mathematics. The area of applications of generalized coherent states is very wide, and a comprehensive exposition of the results in the field would be helpful. This monograph is the first attempt toward this aim. My purpose was to compile and expound systematically the vast amount of material dealing with the coherent states and available through numerous journal articles. The book is based on a number of undergraduate and postgraduate courses I delivered at the Moscow Physico-Technical Institute. In its present form it is intended for professional mathematicians and theoretical physicists; it may also be useful for university students of mathematics and physics. In Part I the formalism is elaborated and explained for some of the simplest typical groups. Part II contains more sophisticated material; arbitrary Lie groups and symmetrical spaces are considered. A number of examples from various areas of theoretical and mathematical physics illustrate advantages of this approach, in Part III.

Coherent states --- Lie groups --- Symmetric spaces --- Mathematical physics --- Groupes de Lie --- Espaces symétriques --- Physique mathématique --- Coherent states. --- Lie groups. --- Mathematical physics. --- Symmetric spaces. --- Espaces symétriques --- Physique mathématique --- Cohérence (physique nucléaire) --- Lie, Groupes de --- Cohérence (physique nucléaire)

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Topological groups. Lie groups --- Ordinary differential equations --- Differential equations --- Lie groups --- Equations différentielles --- Groupes de Lie --- Differential equations. --- Lie groups. --- Equations différentielles --- Mechanics, Analytic. --- Mécanique analytique. --- Hamiltonian systems. --- Systèmes hamiltoniens. --- Differential equations, Nonlinear --- Équations différentielles non linéaires --- Lie, Groupes de --- Lie algebras --- Lie, Algèbres de --- Équations aux dérivées partielles --- Differential equations, Nonlinear. --- Lie algebras. --- Équations aux dérivées partielles --- Équations différentielles non linéaires. --- Lie, Algèbres de --- Mécanique analytique --- Systèmes hamiltoniens --- Application des groupes a la physique