[1]周玉兰,赵丹丹.交互作用Fock空间l2(Γ)上的湮灭算子和增生算子[J].四川师范大学学报(自然科学版),2018,(03):338-342.[doi:10.3969/j.issn.1001-8395.2018.03.010]
 ZHOU Yulan,ZHAO Dandan.The Annihilator Operator and the Creator Operator on the Interacting Fock Space l2(Γ)[J].Journal of SichuanNormal University,2018,(03):338-342.[doi:10.3969/j.issn.1001-8395.2018.03.010]
点击复制

交互作用Fock空间l2(Γ)上的湮灭算子和增生算子()
分享到:

《四川师范大学学报(自然科学版)》[ISSN:1001-8395/CN:51-1295/N]

卷:
期数:
2018年03期
页码:
338-342
栏目:
基础理论
出版日期:
2018-03-15

文章信息/Info

Title:
The Annihilator Operator and the Creator Operator on the Interacting Fock Space l2(Γ)
文章编号:
1001-8395(2018)03-0338-05
作者:
周玉兰 赵丹丹
西北师范大学 数学与统计学院, 甘肃 兰州 730070
Author(s):
ZHOU Yulan ZHAO Dandan
College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, Gansu
关键词:
交互作用Fock空间 增生算子 湮灭算子
Keywords:
the interacting Fock space the creator operator the annihilator operator
分类号:
O177
DOI:
10.3969/j.issn.1001-8395.2018.03.010
文献标志码:
A
摘要:
研究基于l2(N)上交互作用Fock空间l2(Γ)中湮灭算子和增生算子的性质.首先,定义在l2(N)(N上实值平方可和函数所构成的Hilbert空间)上的交互作用Fock空间l2(Γ); 然后,在该空间l2(Γ)中定义湮灭算子和增生算子; 最后,研究此定义之下湮灭算子和增生算子的性质.研究表明:该空间中的湮灭算子和增生算子是有界线性算子且是单位算子,它们除了具有不同位置的交换关系外,还具有相同位置的反交换关系.
Abstract:
In this paper, we present the properties of annihilator and creator operators on the interacting Fock space l2(Γ). First, we define the interacting Fock space l2(Γ)based on l2(N)(l2(N)Nnotes the Hilbert space of all real-value square summable function on N), and then introduce the annihilator operator and the creator operator, we also prove the main results of operators in our context. We show that the annihilator operator is a bounded linear unit operator, the same to the creator operator. In addition, they have the canonical commutation relations in different positions and they satisfy the canonical anti-commutation relations in the same position as well.

参考文献/References:

[1] ACCARDI L, LU Y G. The Wigner semi-circle law in quantum electrodynamics[J]. Communications in Mathematical Physics,1996,180(3):605-632.
[2] ACCARDI L, LU Y G, VOLOVICH I. The QED Hilbert module and interacting Fock spaces[DB/OL].
[2016-08-10]. http://www.researchgate.net/publication/282284148,1997-01.
[3] XU Q H. Remarks on interacting Fock spaces[J]. Infinite Dimensional Ayalysis, Quantum Probability and Related Topics,2000,3(1):191-198.
[4] ASAI N. Analytic characterization of one-mode interacting Fock space[J]. Infinite Dimensional Analysis, Quantum Probability and Related Topics,2001,4(3):409-415.
[5] ACCARDI L, KUO H H, STAN A. Characterization of probability measures through the canonically associated interacting Fock spaces[J]. Infinite Dimensional Ayalysis, Quantum Probability and Related Topics,2004,7(4):485-505.
[6] CRISMALE V. Quantum stochastic calculus on interacting Fock spaces:semimartingale estimates and stochastic integral[J]. Communications on Stochastic Analysis,2007,1(2):321-341.
[7] ACCARDI L, KUO H H, STAN A. An interacting Fock space characterization of probability measures[J]. Communications on Stochastic Analysis,2009,3(1):85-99.
[8] ACCARDI L, BO(·overZ)EJKO M. Interacting Fock spaces and gaussianization of probability measure[J]. Infinite Dimensional Analysis, Quantum Probability and Related Topics,1998,1(4):663-670
[9] KANG Y B, WANG C S. Quantum stochastic integral representations on interacting Fock space[J]. J Theoretical Probability,2015,28(3):1007-1027.
[10] WANG C S, CHAI H F, LU Y C. Discrete-time quantum Bernoulli noises[J]. J Mathematical Physics,2010,51(5):23.
[11] WANG C S, LU Y C, CHAI H F. An alternative approach to Privault's discrete-time chaotic calculus[J]. J Math Anal Appl,2011,373(2):643-654.
[12] 黄志远,王才士,让光林. 量子白噪声分析[M]. 武汉:湖北科学技术出版社,2004:13-30.
[13] 程其襄,张奠宙,魏国强,等. 实变函数与泛函分析基础[M]. 3版. 北京:高等教育出版社,2010:260-261.

相似文献/References:

[1]李红梅.广义Lipschitz增生算子方程的具有误差的Ishikawa迭代的收敛性和稳定性[J].四川师范大学学报(自然科学版),2003,(02):116.
 LI Hong mei(College of Mathematics and Software Science,Sichuan Normal University,Chengdu 00,et al.[J].Journal of SichuanNormal University,2003,(03):116.
[2]谷峰.增生型非线性方程的具混合误差项的Ishikawa迭代程序的收敛性和稳定性[J].四川师范大学学报(自然科学版),2003,(03):257.
 GU Feng (Department of Mathematics,Qiqihar University,Qiqihar 00,et al.[J].Journal of SichuanNormal University,2003,(03):257.
[3].四川师范大学学报(自然科学版)2003年1~6期总目次[J].四川师范大学学报(自然科学版),2003,(06):664.
[4].四川师范大学学报(自然科学版)2004年1~6期总目次[J].四川师范大学学报(自然科学版),2004,(06):664.
[5]金茂明.增生算子方程解的具误差的Ishikawa迭代逼近[J].四川师范大学学报(自然科学版),2002,(04):373.
 JIN Mao ming (Department of Mathematics,Fuling Teachers College,Fuling 0800,et al.[J].Journal of SichuanNormal University,2002,(03):373.
[6].四川师范大学学报(自然科学版)1993年1—6期总目次[J].四川师范大学学报(自然科学版),1993,(06):0.

备注/Memo

备注/Memo:
收稿日期:2017-07-27 接受日期:2017-12-04
基金项目:国家自然科学基金(11461061)
第一作者简介:周玉兰(1979—),女,副教授,主要从事随机分析的研究,E-mail:zhouylw123@163.com
更新日期/Last Update: 2018-03-15