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Lie group
About: Lie group is a research topic. Over the lifetime, 18359 publications have been published within this topic receiving 381012 citations.
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TL;DR: In this article, a generalized method of dimensional reduction, applicable to theories in curved space, is described, where the extra dimensions are related to the manifold of a Lie group and the resulting theory has no cosmological constant, a well-behaved potential, and a number of arbitrary mass parameters.
1,262 citations
Book•
01 Jan 1993
TL;DR: In this article, the authors present a general theory of Lie Derivatives and their application in a variety of fields and functions, including bundles and bundles of bundles on manifolds.
Abstract: I. Manifolds and Lie Groups.- II. Differential Forms.- III. Bundles and Connections.- IV. Jets and Natural Bundles.- V. Finite Order Theorems.- VI. Methods for Finding Natural Operators.- VII. Further Applications.- VIII. Product Preserving Functors.- IX. Bundle Functors on Manifolds.- X. Prolongation of Vector Fields and Connections.- XI. General Theory of Lie Derivatives.- XII. Gauge Natural Bundles and Operators.- References.- List of symbols.- Author index.
1,251 citations
TL;DR: In this paper, the concept of coherent states originally closely related to the nilpotent group of Weyl is generalized to arbitrary Lie groups and its features are investigated for the simplest Lie groups.
Abstract: The concept of coherent states originally closely related to the nilpotent group of Weyl is generalized to arbitrary Lie group. For the simplest Lie groups the system of coherent states is constructed and its features are investigated.
1,174 citations
TL;DR: In this paper, a model based on the bilinear products of creation and annihilation operators can be considered as generators of Lie groups and the problem of finding eigenvalues can be greatly simplified by the additional integrals of the motion which are present if the Hamiltonian is constructed so as to commute with invariants of the group.
1,165 citations
1,153 citations