Journal ArticleDOI
Applications of infinite-dimensional differential geometry to general relativity
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This article is published in Rivista Del Nuovo Cimento.The article was published on 1978-07-01. It has received 8 citations till now. The article focuses on the topics: Four-force & Mathematics of general relativity.read more
Citations
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A Hamiltonian structure of the interacting gravitational and matter fields
TL;DR: In this paper, a Hamiltonian formulation for classical field theories is presented, in which the Hamilton equation is written by means of the energy-momentum function E and the symplectic 2−form Ω.
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Natural bundles. I. A minimal resolution of superspace
TL;DR: In this article, the singularities in the space of geometries or superspace of a closed manifold M have been studied in the context of spin and diffeomorphism group, the Yang-Mills moduli space, and nonlinear sigma models.
Posted Content
On Global One-Dimensionality proposal in Quantum General Relativity
TL;DR: In this article, the simple quantum gravity model, based on a new conjecture within the canonically quantized 3+1 general relativity, is presented, which states that matter fields are functionals of an embedding volume form only and reduces the quantum geometrodynamics.
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General relativity as a generalized Hamiltonian system
TL;DR: In this article, a rigorous setting for Dirac's generalized Hamiltonian dynamics in an infinite number of dimensions is presented, and it is shown that the dynamical formulation of general relativity fits into this scheme.
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Macrostates thermodynamics and its stable classical limit in Global One-Dimensional Quantum General Relativity
TL;DR: In this article, a toy model with nontrivial field theoretical content, describing classical one-dimensional massive bosonic fields related to any 3+1 metric, where the dimension is a volume of three-dimensional embedding, is presented.
References
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Book
Foundations of mechanics
TL;DR: In this article, Ratiu and Cushman introduce differential theory calculus on manifolds and derive an overview of qualitative and topological properties of differentiable properties of topological dynamics.
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Quantum Theory of Gravity. I. The Canonical Theory
TL;DR: In this article, a 6-dimensional hyperbolic Riemannian manifold is introduced, which takes for its metric the coefficient of the momenta in the Hamiltonian constraint and the geodesic incompletability of this manifold, owing to the existence of a frontier of infinite curvature, is demonstrated.