The Hodge-Star Operator

2015 ◽  
pp. 323-328
Keyword(s):  
Hodge Star Operator

scholarly journals The Hodge star operator on Schubert forms

Topology ◽  
2002 ◽  
Vol 41 (5) ◽  
pp. 945-960
Author(s):  
Klaus Künnemann ◽  
Harry Tamvakis
Keyword(s):  
Hodge Star Operator

scholarly journals A FERMIONIC HODGE STAR OPERATOR

1999 ◽  
Vol 14 (15) ◽  
pp. 965-976
Author(s):  
ALFRED DAVIS ◽  
TRISTAN HÜBSCH
Keyword(s):  
Field Theory ◽  
Wave Function ◽  
Bilinear Form ◽  
Operator Representation ◽  
Exterior Calculus ◽  
Star Operation ◽  
Hodge Star Operator

A fermionic analogue of the Hodge star operation is shown to have an explicit operator representation in models with fermions, in space–times 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 identical to the standard one constructed using hermitian conjugation; the utility of the induced complex bilinear form remains unclear.

The Poincaré Map in Mixed Exterior Algebra

1983 ◽  
Vol 26 (2) ◽  
pp. 129-136 ◽  
Author(s):  
J. R. Vanstone
Keyword(s):  
Linear Algebra ◽  
Poincaré Map ◽  
Exterior Algebra ◽  
Poincare Map ◽  
New Formula ◽  
Hodge Star Operator

AbstractThe Poincaré map of mixed exterior algebra generalizes the Hodge star operator and it plays a central rôle in the proofs of many classical identities of linear algebra. The principal purpose of this paper is to derive a new formula for it. This formula is useful in circumstances when the definition is too implicit. Several applications are discussed.

scholarly journals Homogeneous and Inhomogeneous Maxwell’s Equations in Terms of Hodge Star Operator

2018 ◽  
Vol 37 ◽  
pp. 15-27
Author(s):  
Zakir Hossine ◽  
Md Showkat Ali
Keyword(s):  
Riemannian Manifolds ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Differential Forms ◽  
Flat Space ◽  
Space Time ◽  
Exterior Algebra ◽  
Important Ingredient ◽  
Maxwell’S Equation ◽  
Hodge Star Operator

The main purpose of this work is to provide application of differential forms in physics. For this purpose, we describe differential forms, exterior algebra in details and then we express Maxwell’s equations by using differential forms. In the theory of pseudo-Riemannian manifolds there will be an important operator, called Hodge Star Operator. Hodge Star Operator arises in the coordinate free formulation of Maxwell’s equation in flat space-time. This operator is an important ingredient in the formulation of Stoke’stheorem.GANIT J. Bangladesh Math. Soc.Vol. 37 (2017) 15-27

scholarly journals The WeitzenbÕck formula for the Bach operator

1995 ◽  
Vol 137 ◽  
pp. 149-181 ◽  
Author(s):  
Mitsuhiro Itoh
Keyword(s):  
Riemannian Metrics ◽  
The Self ◽  
Weitzenböck Formula ◽  
Hodge Star Operator

(Anti-)self-dual metrics are 4-dimensional Riemannian metrics whose Weyl conformai tensor W half vanishes. The Weyl conformai tensor W of an arbitrary metric on an oriented 4-manifold has in general the self-dual part W+ and the anti-self-dual part W− with respect to the Hodge star operator * and one says that a metric is self-dual or anti-self-dual if W− = 0 or W+ = 0, respectively.

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