# Newton-Leibniz integration for ket-bra operators (III)-Application in fermionic quantum statistics

## Abstract

The Newton-Leibniz integration over Dirac's ket-bra operators introduced in Ref. [Hong-yi Fan, Hai-liang Lu, Yue Fan, Ann. Phys. 321 (2006) 480-494] is generalized to Newton-Leibniz-Berezin integration over fermionic ket-bra 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 multi-mode quadratic interacting fermion is derived via the fermionic coherent state representation and the IWOP technique. The two-mode 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 Bose-Fermi 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). E-mail: 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: S0003-4916(06)00218-1; 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.
```*Newton-Leibniz integration for ket-bra operators (III)-Application in fermionic quantum statistics*. United States: N. p., 2007.
Web.

```
Fan Hongyi.
```*Newton-Leibniz integration for ket-bra operators (III)-Application in fermionic quantum statistics*. United States.

```
Fan Hongyi. Sun .
"Newton-Leibniz integration for ket-bra operators (III)-Application in fermionic quantum statistics". United States.
doi:.
```

```
@article{osti_20976748,
```

title = {Newton-Leibniz integration for ket-bra operators (III)-Application in fermionic quantum statistics},

author = {Fan Hongyi},

abstractNote = {The Newton-Leibniz integration over Dirac's ket-bra operators introduced in Ref. [Hong-yi Fan, Hai-liang Lu, Yue Fan, Ann. Phys. 321 (2006) 480-494] is generalized to Newton-Leibniz-Berezin integration over fermionic ket-bra 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 multi-mode quadratic interacting fermion is derived via the fermionic coherent state representation and the IWOP technique. The two-mode 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 Bose-Fermi 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}

}