منابع مشابه
A 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 کاملThe 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 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...
متن کاملDelaunay Hodge star
We define signed dual volumes at all dimensions for circumcentric dual meshes. We show that for pairwise Delaunay triangulations with mild boundary assumptions these signed dual volumes are positive. This allows the use of such Delaunay meshes for Discrete Exterior Calculus (DEC) because the discrete Hodge star operator can now be correctly defined for such meshes. This operator is crucial for ...
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.
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ژورنال
عنوان ژورنال: Modern Physics Letters A
سال: 1999
ISSN: 0217-7323,1793-6632
DOI: 10.1142/s0217732399001036