منابع مشابه
The Hodge Star Operator
We’ll start out by defining the Hodge star operator as a map from ∧k(R) to ∧n−k(R). Here ∧k(R) denotes the vector space of alternating k-tensors on R. Later on, we will extend this definition to alternating tensors on a finite dimensional vector space that is equipped with an inner product. Let I = (i1, ..., ik) be some increasing multi-index of length k. That is i1 < i2 < i3 < .... Let J = (j1...
متن کاملA Fermionic Hodge Star Operator
A fermionic analogue of the Hodge star operation is shown to have an explicit operator representation in models with fermions, in spacetimes of any dimension. This operator realizes a conjugation (pairing) not used explicitly in field-theory, and induces a metric in the space of wave-function(al)s just as in exterior calculus. If made real (Hermitian), this induced metric turns out to be identi...
متن کامل. A G ] 2 9 Ju n 20 03 THE HODGE STAR OPERATOR ON SCHUBERT FORMS
Let X = G/P be a homogeneous space of a complex semisimple Lie group G equipped with a hermitian metric. We study the action of the Hodge star operator on the space of harmonic differential forms on X. We obtain explicit combinatorial formulas for this action when X is an irreducible hermitian symmetric space of compact type.
متن کاملThe Suslin operator in applicative theories reconsidered
The Suslin operator E1 is a type-2 functional testing for the wellfoundedness of binary relations on the natural numbers. In the context of applicative theories, its proof-theoretic strength has been analyzed in Jäger and Strahm [18]. This article provides a more direct approach to the computation of the upper bounds in question. Several theories featuring the Suslin operator are embedded into ...
متن کاملThe Hodge Dual Operator
The Hodge dual operator ∗ is one of the 3 basic operations on differential forms. (The other 2 are wedge product ∧ and exterior differentiation d.) However most treatments consider only positive-definite inner products, and there are at least 2 standard ways of generalizing this to inner products of arbitrary signature. We outline here a construction of the Hodge dual operator which works for a...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2014
ISSN: 0024-3795
DOI: 10.1016/j.laa.2014.03.039