A geometrically defined discrete hodge operator on simplicial cells

2006 ◽  
Vol 42 (4) ◽  
pp. 643-646 ◽  
Author(s):  
B. Auchmann ◽  
S. Kurz
Keyword(s):  
Hodge Operator

AN ${\rm SL}(2, {\mathbb C})$ ACTION ON CHIRAL RINGS AND THE MIRROR MAP

1992 ◽  
Vol 07 (35) ◽  
pp. 3277-3289 ◽  
Author(s):  
TRISTAN HÜBSCH ◽  
SHING-TUNG YAU
Keyword(s):  
Complex Structure ◽  
Inner Product ◽  
General Definition ◽  
Canonical Class ◽  
Hodge Operator ◽  
Volume Limit ◽  
Chiral Rings ◽  
Lefschetz Type ◽  
Definition Of ◽  
Mirror Map

Each transversal degree-d hypersurface ℳ in a weighted projective space defines a Landau-Ginzburg orbifold, the superpotential of which equals the defining polynomial of ℳ. For a generic such ℳ with trivial canonical class, the degree-0 (mod d) subring of the Jacobian ring (that is, the (c, c)-ring of the Landau-Ginzburg orbifold) is shown to admit an [Formula: see text] action and the corresponding Lefschetz-type decomposition. This leads to a general definition of a “large complex structure” limit, the mirror of the “large volume” limit, and the mirror images on ⊕qH3−q,q of the Hodge *-operator, duality and inner product on ⊕qHq,q.

The Hodge Operator in Fermionic Fock Space

2005 ◽  
Vol 70 (7) ◽  
pp. 979-1016 ◽  
Author(s):  
Leszek Z. Stolarczyk
Keyword(s):  
Fock Space ◽  
Differential Forms ◽  
Grassmann Algebra ◽  
Basis Set ◽  
Electron Systems ◽  
Linear Transformations ◽  
Spin Orbital ◽  
Creation And Annihilation Operators ◽  
Finite Dimensional ◽  
Hodge Operator

The Hodge operator ("star" operator) plays an important role in the theory of differential forms, where it serves as a tool for the switching between the exterior derivative and co-derivative. In the theory of many-electron systems involving a finite-dimensional fermionic Fock space, one can define the Hodge operator as a unique (i.e., invariant with respect to linear transformations of the spin-orbital basis set) antilinear operator. The similarity transformation based on the Hodge operator results in the switching between the fermion creation and annihilation operators. The present paper gives a self-contained account on the algebraic structures which are necessary for the construction of the Hodge operator: the fermionic Fock space, the corresponding Grassmann algebra, and the generalized creation and annihilation operators. The Hodge operator is then defined, and its properties are reviewed. It is shown how the notion of the Hodge operator can be employed in a construction of the electronic time-reversal operator.

Hodge Operator

2004 ◽  
pp. 189-189
Author(s):  
Thomas Chen ◽  
Jürgen Fuchs ◽  
Steven Duplij ◽  
Evgeniy Ivanov ◽  
Steven Duplij ◽  
...  
Keyword(s):  
Hodge Operator

Algebraic Second Order Hodge Operator for Poisson's Equation

2013 ◽  
Vol 49 (5) ◽  
pp. 1761-1764 ◽  
Author(s):  
Piergiorgio Alotto ◽  
Fabio Freschi ◽  
Maurizio Repetto
Keyword(s):  
Second Order ◽  
Poisson’S Equation ◽  
Poisson's Equation ◽  
Hodge Operator

Algebraic Cycles in Families of Abelian Varieties

1994 ◽  
Vol 46 (06) ◽  
pp. 1121-1134 ◽  
Author(s):  
Salman Abdulali
Keyword(s):  
Abelian Varieties ◽  
Algebraic Cycles ◽  
Hodge Conjecture ◽  
Hodge Operator

Abstract If the Hodge *-operator on the L2-cohomology of Kuga fiber varieties is algebraic, then the Hodge conjecture is true for all abelian varieties.

Time Domain Electromagnetic Differential Equation Methods

2012 ◽  
Vol 490-495 ◽  
pp. 840-844
Author(s):  
Yong Sheng Xu ◽  
Li Kong
Keyword(s):  
Differential Equation ◽  
Time Domain ◽  
Discrete Equations ◽  
Hodge Operator ◽  
Time Domain Electromagnetic ◽  
The Time Domain

As the time domain electromagnetic differential equation methods, FDTD, FIT, TDFEM have some relations in the mesh generations, discrete equations and hodge operator.

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