The Hodge Operator in Fermionic Fock Space

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Title:The Hodge Operator in Fermionic Fock Space
Creators:
Stolarczyk, Leszek Z.
Journal or Publication Title:
Collection of Czechoslovak Chemical Communications, 70, 7, pp. 979-1016
Uncontrolled Keywords:Spin-orbital bases, Hodge operator, Fock space, Grassmann algebra, Many-electron systems, Time-reversal operator, Quantum chemistry, Fermions

Abstract

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. <p>

Title:The Hodge Operator in Fermionic Fock Space
Creators:
Stolarczyk, Leszek Z.
Uncontrolled Keywords:Spin-orbital bases, Hodge operator, Fock space, Grassmann algebra, Many-electron systems, Time-reversal operator, Quantum chemistry, Fermions
Divisions:Life and Chemical Sciences > Institute of Organic Chemistry and Biochemistry > Collection of Czechoslovak Chemical Communications
Journal or Publication Title:Collection of Czechoslovak Chemical Communications
Volume:70
Number:7
Page Range:pp. 979-1016
ISSN:0010-0765
E-ISSN:1212-6950
Publisher:Institute of Organic Chemistry and Biochemistry
Related URLs:
URLURL Type
http://dx.doi.org/10.1135/cccc20050979UNSPECIFIED
ID Code:2402
Item Type:Article
Deposited On:06 Feb 2009 17:18
Last Modified:06 Feb 2009 16:18

Citation

Stolarczyk, Leszek Z. (2005) The Hodge Operator in Fermionic Fock Space. Collection of Czechoslovak Chemical Communications, 70 (7). pp. 979-1016. ISSN 0010-0765

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