Noether Identities at the Quantum Level

LI Zi-Ping

近期发现有不法分子冒充我刊与作者联系，借此进行欺诈等不法行为，请广大作者加以鉴别，如遇诈骗行为，请第一时间与我刊编辑部联系确认（《中国物理C》（英文）编辑部电话：010-88235947,010-88236950），并作报警处理。

本刊再次郑重声明：

（1）本刊官方网址为cpc.ihep.ac.cn和https://iopscience.iop.org/journal/1674-1137

（2）本刊采编系统作者中心是投稿的唯一路径，该系统为ScholarOne远程稿件采编系统，仅在本刊投稿网网址（https://mc03.manuscriptcentral.com/cpc）设有登录入口。本刊不接受其他方式的投稿，如打印稿投稿、E-mail信箱投稿等，若以此种方式接收投稿均为假冒。

（3）所有投稿均需经过严格的同行评议、编辑加工后方可发表，本刊不存在所谓的“编辑部内部征稿”。如果有人以“编辑部内部人员”名义帮助作者发稿，并收取发表费用，均为假冒。

《中国物理C》（英文）编辑部

2024年10月30日

Chinese Physics C> 2002, Vol. 26> Issue(3) : 230-238

Noether Identities at the Quantum Level

LI Zi-Ping ^,

College of Applied Science, Beijing Polytechnic University, Beijing 100022, China

Abstract
HTML
Reference
Related

PDF

Abstract：
Based on the phase-space generating functional of Green function, the canonical Noether identities under the local transformation at the quantum level have been derived. For the gauge-invariant system, the quantal Noether identities in configuration space have been also deduced. It is pointed out that in certain cases the quantal Noether identities may be converted to quantal conservation laws of the system. This method for obtaining the quantal conservation laws is significantly different from the first Noether theorem at the quantum level. The application to non-Abelian CS theories is studied, the quantal conserved BRS and PBRS charges are obtained, and these two conserved charges are totally different.

References

[1]

LI Z P. Classical and Quanta1 Dynamics of Constrained System and Their Symmetry Properties, Beijing, Beijing Polytechnic University Press, 1993(in Chinese)(李子平. 经典和量子约束系统及其对称性质, 北京: 北京工业大学出版社, 1993)2 LI Z P. Int. J. Theor. Phys., 1995.34: 19453 LI Z P. Science in China (Scientia Sinica) , Series A, 1993,36: 12124 LI Z P. Phys. Rev., 1994, E50:8765 LI Z P. Int . J. Theor. PhYS., 1994,33: 12076 LI Z P. Science in China ( Scientia Sinica), Series A. 1996, 39: 7397 LI Z P. Z. Phys., 1997, C76: 1818 Mizrahi M M. J. Math. Phys., 1978, 19: 2989 LI Z P. Int. J. Theor. Phys., 1995, 34: 52310 LI Z P. lnt. J. Theor. Phys., 1987, 26: 85311 Young B L, Introduction to Quantum Field Theories. Beijing, Science Press. 198712 LI Z P. Int. J. Theor. Phys., 1993. 32: 20113 LI Z P. JIANG J H. Symmetries in Constrained Canonid Systems, Beijing, Science Press, 200214 LI Z P, GAO H X. Int. J. Theor. Phys., 1997, 36: 107115 LI Z P, Chinese Science Bulletin, 1999, 44: 20716 Deser S, Jackiw R, Templeton S. Ann. Phys., 1982, 140: 37217 Sundermeyer K. Lecture Notes in Physics. 169. Berlin. Springer-Verlag, 198218 Fossats A. Manavella E, Repetro C et a]. Int. J. Theor. Phys., 1995, 34: 1037; J. Math. Phys., 1996, 37: 8419 LI Z P, LONG Z W. J. Phys., 1999, A32: 6391

[1]	WANG Jing , HUANG Yong-Chang . BRST Transformation Equivalence and Ward Identities of 1+1 Dimensional Non-linear σ Model. Chinese Physics C, 2004, 28(1): 17-21.
[2]	LONG Zheng-Wen , LI Zi-Ping . Canonical Ward Identity and Dynamical Mass Generation in Abelian Gauge Theory. Chinese Physics C, 2004, 28(2): 134-139.
[3]	HUANG Chao-Guang , GUO Han-Ying , WU Xiao-Ning . Noether Theorem and Black Hole's Mass Formula and Entropy. Chinese Physics C, 2003, 27(10): 879-883.
[4]	LI Zi-Ping , LI Rui-Jie . Generalized Ward Identities for Non-local Transformation. Chinese Physics C, 2002, 26(2): 122-128.
[5]	LI Zi-Ping . Non-local Quantal Noether Identities and Their Applications. Chinese Physics C, 2002, 26(12): 1214-1222.
[6]	Li Ziping . Feynman Rules and Generalized Ward Identities in Phase Space Functional Integral. Chinese Physics C, 1996, 20(8): 698-702.
[7]	Li Ziping . Generalization and Application of the Noether's Identities. Chinese Physics C, 1995, 19(S2): 157-163.
[8]	Li Ziping . Canonical Ward Identities in Generalized QCD. Chinese Physics C, 1995, 19(5): 405-412.
[9]	Li Ziping . Generalization of the Noether's Identities and Application. Chinese Physics C, 1995, 19(4): 320-326.
[10]	Li Ziping . Canonical Symmetry in a System with Singular Lagrangian and Ward Identities. Chinese Physics C, 1994, 18(8): 694-701.
[11]	SHEN Kun , QIU Zhong-Ping . Chiral Ward-Takahashi Identities at Finite Temperature and Chiral Phase Transition in (2+1) Dimensional Chiral Gross-Neveu Model. Chinese Physics C, 1993, 17(3): 208-214.
[12]	SHEN Kun , QIU Zhong-Ping . Ward-Takahashi Identities and Mass Spectra in (2+1) Dimensional SU(2) Four-fermi Model. Chinese Physics C, 1993, 17(1): 17-27.
[13]	QIU Rong . The Identity and Renormalization of Pure Gauge Fields in Coset Space of Abelian Chiral Group. Chinese Physics C, 1993, 17(3): 227-240.
[14]	SHEN Kun , QIU Zhong-Ping . Chiral Symmetry,Ward-Takahashi Identities and Mass Spectra in (2+1) Dimensional Chiral Gross-Neveu Model. Chinese Physics C, 1992, 16(1): 29-37.
[15]	LI Zi-Ping . THE GENERALIZED NOETHER'S IDENTITIES AND CONSERVED CHARGE. Chinese Physics C, 1988, 12(6): 782-785.
[16]	ZHANG Yue-Zhong . AXIAL VECTOR WARD IDENTITIES AND DIMENSIONAL REGULARIZATION IN RENORMALIZABLE SU(2)_L×U(1)_Y MODEL. Chinese Physics C, 1985, 9(4): 430-436.
[17]	LI JIAN-PING , CHANG WUI-KE , XIE YAN-FONG , TANG JIN-HUA , TANG E-SHENG . MEASUREMENT OF NATURAL BACKGROUND NEUTRON. Chinese Physics C, 1982, 6(6): 665-670.
[18]	Kuang Yu-ping , Yi Yu-ping . WARD-TAKAHASHI IDENTITIES FOR GAUGE.GHOST FIELD PROPER VERTICES. Chinese Physics C, 1980, 4(3): 286-290.
[19]	ZHOU GUANG-ZHAO , SU ZHAO-BING . ON THE DYSON EQUATION AND THE WARD-TAKAHASHI IDENTITIES OF THE CLOSED TIME PATH GREEN'S FUNCTIONS. Chinese Physics C, 1979, 3(3): 314-326.
[20]	WANG RONG . A PROOF OF TWO IDENTITIES CONCERNING THE INTERCHANGE IN THE ORDER OF INTEGRATIONS. Chinese Physics C, 1979, 3(5): 645-650.

Access

Get Citation

LI Zi-Ping. Noether Identities at the Quantum Level[J]. Chinese Physics C, 2002, 26(3): 230-238.

LI Zi-Ping. Noether Identities at the Quantum Level[J]. Chinese Physics C, 2002, 26(3): 230-238. shu

RIS(for EndNote,Reference Manager,ProCite)

BibTex

Txt

Milestone

Received: 2001-05-18
Revised: 1900-01-01

Article Metric

Article Views(2588)
PDF Downloads(618)
Cited by(0)

Policy on re-use

To reuse of subscription content published by CPC, the users need to request permission from CPC, unless the content was published under an Open Access license which automatically permits that type of reuse.

通讯作者: 陈斌, bchen63@163.com

1.
沈阳化工大学材料科学与工程学院沈阳 110142

Noether Identities at the Quantum Level

LI Zi-Ping ^,

Corresponding author: LI Zi-Ping,

College of Applied Science, Beijing Polytechnic University, Beijing 100022, China

Received Date: 2001-05-18
Accepted Date: 1900-01-01
Available Online: 2002-03-05

Abstract: Based on the phase-space generating functional of Green function, the canonical Noether identities under the local transformation at the quantum level have been derived. For the gauge-invariant system, the quantal Noether identities in configuration space have been also deduced. It is pointed out that in certain cases the quantal Noether identities may be converted to quantal conservation laws of the system. This method for obtaining the quantal conservation laws is significantly different from the first Noether theorem at the quantum level. The application to non-Abelian CS theories is studied, the quantal conserved BRS and PBRS charges are obtained, and these two conserved charges are totally different.