Titlebook: Differential Geometrical Methods in Theoretical Physics; K. Bleuler,M. Werner Book 1988 Springer Science+Business Media Dordrecht 1988 The

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https://doi.org/10.1007/978-3-030-21799-0The approach of J.Douglas to Plateau’s problem is here reviewed with an eye to physical applications. It is shown that the functional of Douglas is related to the wave function of the string in a manner which closely resembles the one proposed by Hawking for the wave function of the Universe.

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Review of Rapid OKP Product DevelopmentThe phase space of Hamiltonean systems is a symplectic manifold (M, .). Let a Lie group G act on (M, .) by symplectic automorphisms. The momen tum map . provides a geometric formulation of the relationship between symmetries and conserved quantities. It is a map . where .. is the dual of the Lie algebra .. of G, defined in the following way: ..

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On ,,The simply-laced exceptional simple Lie algebras form part of an infinite series of Kac-Moody Lie algebras . with Coxeter-Dynkin diagrams ..,. ≥ 3, of the form

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On Strings and J.Douglas Variational PrincipleThe approach of J.Douglas to Plateau’s problem is here reviewed with an eye to physical applications. It is shown that the functional of Douglas is related to the wave function of the string in a manner which closely resembles the one proposed by Hawking for the wave function of the Universe.

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Singular Points in Level Sets of the Momentum Map and Quantum TheoryThe phase space of Hamiltonean systems is a symplectic manifold (M, .). Let a Lie group G act on (M, .) by symplectic automorphisms. The momen tum map . provides a geometric formulation of the relationship between symmetries and conserved quantities. It is a map . where .. is the dual of the Lie algebra .. of G, defined in the following way: ..

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The Impact of Physics on Geometry Floer on 3-manifolds. Solvable models in statistical mechanics have been used by Vaughan Jones to construct polynomial invariants of knots. String theory has produced a new connection between manifolds and modular forms. In all cases it is quantum theory that ties in with topology.

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Weyl’s Program and Modern Physicsd at some length in the reference cited at the end of section IV. This article is in part an exposition of the relationship of this program to one formulated by Weyl in 1927, in part a review and revision of material from the reference mentioned above and in part a description of ideas and incomplete work relevant to carrying the program further.