NewtonLeibniz integration for ketbra operators (III)Application in fermionic quantum statistics
Abstract
The NewtonLeibniz integration over Dirac's ketbra operators introduced in Ref. [Hongyi Fan, Hailiang Lu, Yue Fan, Ann. Phys. 321 (2006) 480494] is generalized to NewtonLeibnizBerezin integration over fermionic ketbra projection operators, the corresponding technique of integration within an ordered product (IWOP) of Fermi operators is proposed which is then used to develop fermionic quantum statistics. The generalized partition function formula of multimode quadratic interacting fermion is derived via the fermionic coherent state representation and the IWOP technique. The twomode fermionic squeezing operators and their group property studied by their fermionic coherent state representation as well as fermionic permutation operator are also deduced in this way. Thus Dirac's symbolic method for Fermi system can also be developed, which exhibits BoseFermi supersymmetry in this aspect.
 Authors:
 CCAST (World laboratory), P.O. Box 8730, Beijing 100080 (China) and Department of Material Science and Engineering, University of Science and Technology of China, Hefei, Anhui 230026 (China) and Department of Physics, Shanghai Jiao Tong University, Shanghai 200030 (China). Email: fhym@ustc.edu.cn
 Publication Date:
 OSTI Identifier:
 20976748
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Annals of Physics (New York); Journal Volume: 322; Journal Issue: 4; Other Information: DOI: 10.1016/j.aop.2006.10.002; PII: S00034916(06)002181; Copyright (c) 2006 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved; Country of input: International Atomic Energy Agency (IAEA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ANNIHILATION OPERATORS; EIGENSTATES; FERMIONS; PARTITION FUNCTIONS; PROJECTION OPERATORS; QUANTUM MECHANICS; STATISTICS; SUPERSYMMETRY
Citation Formats
Fan Hongyi. NewtonLeibniz integration for ketbra operators (III)Application in fermionic quantum statistics. United States: N. p., 2007.
Web.
Fan Hongyi. NewtonLeibniz integration for ketbra operators (III)Application in fermionic quantum statistics. United States.
Fan Hongyi. Sun .
"NewtonLeibniz integration for ketbra operators (III)Application in fermionic quantum statistics". United States.
doi:.
@article{osti_20976748,
title = {NewtonLeibniz integration for ketbra operators (III)Application in fermionic quantum statistics},
author = {Fan Hongyi},
abstractNote = {The NewtonLeibniz integration over Dirac's ketbra operators introduced in Ref. [Hongyi Fan, Hailiang Lu, Yue Fan, Ann. Phys. 321 (2006) 480494] is generalized to NewtonLeibnizBerezin integration over fermionic ketbra projection operators, the corresponding technique of integration within an ordered product (IWOP) of Fermi operators is proposed which is then used to develop fermionic quantum statistics. The generalized partition function formula of multimode quadratic interacting fermion is derived via the fermionic coherent state representation and the IWOP technique. The twomode fermionic squeezing operators and their group property studied by their fermionic coherent state representation as well as fermionic permutation operator are also deduced in this way. Thus Dirac's symbolic method for Fermi system can also be developed, which exhibits BoseFermi supersymmetry in this aspect.},
doi = {},
journal = {Annals of Physics (New York)},
number = 4,
volume = 322,
place = {United States},
year = {Sun Apr 15 00:00:00 EDT 2007},
month = {Sun Apr 15 00:00:00 EDT 2007}
}

We show that the technique of integration within normal ordering of operators [Hongyi Fan, Hailiang Lu, Yue Fan, Ann. Phys. 321 (2006) 480494] applied to tackling NewtonLeibniz integration over ketbra projection operators, can be generalized to the technique of integration within Weyl ordered product (IWWOP) of operators. The Weyl ordering symbol is introduced to find the Wigner operator's Weyl ordering form {delta}(p,q) = {delta}(p  P){delta}(q  Q) , and to find operators' Weyl ordered expansion formula. A remarkable property is that Weyl ordering of operators is covariant under similarity transformation, so it has many applications in quantum statistics andmore »

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NewtonLeibniz integration for ketbra operators (II)application in deriving density operator and generalized partition function formula
Via the route of applying NewtonLeibniz integration rule to Dirac's symbolic operators, we show that the density operator e{sup {beta}}{sup H}, where H is multimode quadratic interacting boson operators, is a mapping of symplectic transformation in the coherent state representation appearing in the form of nonsymmetric ketbra operator integration. By virtue of the technique of integration within an ordered product (IWOP) of operators, we deduce its normally ordered form which directly leads to the generalized partition function formula and the Wigner function. Some new representations, such as displacementsqueezing correlated squeezed coherent states, constructed by the IWOP technique, also bring conveniencemore »