منابع مشابه
Current Algebras and Differential Geometry
We show that symmetries and gauge symmetries of a large class of 2-dimensional σ-models are described by a new type of a current algebra. The currents are labeled by pairs of a vector field and a 1-form on the target space of the σ-model. We compute the current-current commutator and analyse the anomaly cancellation condition, which can be interpreted geometrically in terms of Dirac structures,...
متن کاملLinear algebra and differential geometry on abstract Hilbert space
Isomorphisms of separable Hilbert spaces are analogous to isomorphisms of n-dimensional vector spaces. However, while n-dimensional spaces in applications are always realized as the Euclidean space Rn, Hilbert spaces admit various useful realizations as spaces of functions. In the paper this simple observation is used to construct a fruitful formalism of local coordinates on Hilbert manifolds. ...
متن کاملDifferential Geometry of the Lie algebra of the quantum plane
We present a differential calculus on the extension of the quantum plane obtained considering that the (bosonic) generator x is invertible and furthermore working polynomials in ln x instead of polynomials in x. We call quantum Lie algebra to this extension and we obtain its Hopf algebra structure and its dual Hopf algebra.
متن کاملClifford Algebra, Geometry and Physics
The geometric calculus based on Clifford algebra is a very useful tool for geometry and physics. It describes a geometric structure which is much richer than the ordinary geometry of spacetime. A Clifford manifold (C-space) consists not only of points, but also of 1-loops, 2-loops, etc.. They are associated with multivectors which are the wedge product of the basis vectors, the generators of Cl...
متن کاملAlgebra and Geometry of Rewriting
We present various results of the last twenty years converging towards a homotopical theory of computation. This new theory is based on two crucial notions : polygraphs (introduced by Albert Burroni) and polygraphic resolutions (introduced by François Métayer). There are two motivations for such a theory: • providing invariants of computational systems to study those systems and prove propertie...
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ژورنال
عنوان ژورنال: Journal of High Energy Physics
سال: 2005
ISSN: 1029-8479
DOI: 10.1088/1126-6708/2005/03/035