Global Symmetry and Quantal Conservation Laws for a Gauge-Invariant System With a Higher-Order Lagrangian

LONG ZhengWen; Li ZiPing

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《中国物理C》（英文）编辑部

2024年10月30日

Chinese Physics C> 2000, Vol. 24> Issue(2) : 106-112

Global Symmetry and Quantal Conservation Laws for a Gauge-Invariant System With a Higher-Order Lagrangian

LONG ZhengWen ^, ,
Li ZiPing

Department of Physics-Electronics, Guizhou University, Guiyang 550025, China2 Department of Applied Physics,Beijing Polytechnic University, Beijing 100022,China

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Abstract：
Based on the configuration-space generating functional obtained by using the Faddeev-Popov trick for a gauge-invariant system and phase- space generating functional obtained by using the Faddeev-Senjanovic method for a constrained Hamiltonian system with a singular higher order Lagrangian respectively, the conservation laws at the quantum level were derived. A preliminary application of the present formulation to the higher-order Maxwell non-Abelian Chern-Sinons(CS) theory is given,the quantal BRS conserved charge and quantal angular momentum for higher-order Maxwell non-Abelian CS term coupled to scalar fields were obtained. The results arising from configuration space generating functional coincide with the result deriving from phase-space generating functional,and the quantal conserved angular momentum differ from the classical one in that one needs to take into account the contribution of the the angular momentum of ghost fields in Maxwell non-Abelian CS theories. The fractional spin property for CS theories is discussed.

References

[1]

. LIZiPing .Europhys Lett.,1993,21:141—146 2. LIZiPing .Science in China ,Series A ,1993,36:1212— 1221. (李子平.中国科学,A辑,1993,36:1212—1221) 3. LIZiPing J.Phys.Math.Gen.,1991,A24 :4261—4274 4. Felipe R Gonzalez.Phys.Lett.1998,B417:114—118.5. PrangeR E ,Girvin S M .The Quantum Hall Effect.Berlin :Springer–Verlag ,19906. LI ZiPing ,Classical and Quantal Dynamics of Constrained Systems and Their Symmetry Properties.Beijing:Beijing Poly technic University Press,1993.175— 176 ;354— 355;419— 422 .(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,1993.175—176 ;354— 355;419—422 )7. YOUNG BinLing,Introduction to Quantum Field Theories.Beijing :Science Press,1987,29— 38(杨炳麟.量子场论导引.上册.北京:科学出版社,1988,29—38)8. LI ZiPing.Europhys.Lett.,1994 ,27(8):563—567 9. LI ZiPing.Commun.Theor.Phys.,1997,27( 3):381—38410. Foussats A ,Manavella E ,Repetto C et al.Int.J .Theor.Phys.,1995,34(7) :1037—1053 11. Deser S ,Jackiw R ,Templeton S.Ann .Phys.,1982,140 :372—411 12. Antilon A ,Escalona J,German G et al.Phys.Lett.,1995,B359:327—333

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LONG ZhengWen and Li ZiPing. Global Symmetry and Quantal Conservation Laws for a Gauge-Invariant System With a Higher-Order Lagrangian[J]. Chinese Physics C, 2000, 24(2): 106-112.

LONG ZhengWen and Li ZiPing. Global Symmetry and Quantal Conservation Laws for a Gauge-Invariant System With a Higher-Order Lagrangian[J]. Chinese Physics C, 2000, 24(2): 106-112. shu

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Received: 1998-12-14
Revised: 1900-01-01

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Global Symmetry and Quantal Conservation Laws for a Gauge-Invariant System With a Higher-Order Lagrangian

LONG ZhengWen ^,
Li ZiPing

Corresponding author: LONG ZhengWen,

Department of Physics-Electronics, Guizhou University, Guiyang 550025, China2 Department of Applied Physics,Beijing Polytechnic University, Beijing 100022,China

Received Date: 1998-12-14
Accepted Date: 1900-01-01
Available Online: 2000-02-05

Abstract: Based on the configuration-space generating functional obtained by using the Faddeev-Popov trick for a gauge-invariant system and phase- space generating functional obtained by using the Faddeev-Senjanovic method for a constrained Hamiltonian system with a singular higher order Lagrangian respectively, the conservation laws at the quantum level were derived. A preliminary application of the present formulation to the higher-order Maxwell non-Abelian Chern-Sinons(CS) theory is given,the quantal BRS conserved charge and quantal angular momentum for higher-order Maxwell non-Abelian CS term coupled to scalar fields were obtained. The results arising from configuration space generating functional coincide with the result deriving from phase-space generating functional,and the quantal conserved angular momentum differ from the classical one in that one needs to take into account the contribution of the the angular momentum of ghost fields in Maxwell non-Abelian CS theories. The fractional spin property for CS theories is discussed.