在平面二元树族上的量子电动力学的H-Hopf模
The H-Hopf Module of Quantum Electrodynamics on Planar Binary Tree
DOI: 10.12677/AAM.2015.42022, PDF, HTML, XML, 下载: 2,358  浏览: 9,422  科研立项经费支持
作者: 江妙浩, 任北上, 赵汝菊, 刘君伟:广西师范学院数学与统计科学学院,广西 南宁
关键词: H-Hopf模量子电动力学半直余积重正化余作用H-Hopf Module Quantum Electrodynamics Semidirect Coproduct Renormalization Coaction
摘要: 利用费曼图和平面二元树的结合,定义了QED的重正化群并指出群上半直积的H-Hopf模和H-Hopf模的半直余积,平面二元树上的H-Hopf模的传播及带电的H-Hopf模,最后得出量子电动力学的H-Hopf模及电子和量子的重正化余作用。
Abstract: Using the combination of Feynman diagrams and the planar binary tree, the renormalization group of QED was defined and the H-Hopf module of semidirect product of the group, the semidirect coproduct of the H-Hopf module, the spread of the H-Hopf module on the planar binary tree and the H-Hopf module with charge were pointed out. Finally it concluded the H-Hopf module of quantum electrodynamics and the renormalization coaction of electron and photon.
文章引用:江妙浩, 任北上, 赵汝菊, 刘君伟. 在平面二元树族上的量子电动力学的H-Hopf模[J]. 应用数学进展, 2015, 4(2): 172-181. http://dx.doi.org/10.12677/AAM.2015.42022

参考文献

[1] Beck, I. (1988) Coloring of commutative rings. Journal of Algebra, 116, 208-226.
[2] Schmitt, W.R. (1994) Incidence Hopf algebras. Journal of Pure and Applied Algebra, 96, 299-330.
[3] Schmitt, W.R. (1995) Hopf algebra methods in graph theory. Journal of Pure and Applied Algebra, 101, 77-90.
[4] Anderson, D.F. and Livingston, P.S. (1999) The zero-divisor graph of a commutative ring. Algebra, 217, 434-447.
[5] 邓汉元, 胡国权, 何国梁 (1998) 二元树族的H-Hopf代数结构. 湖南大学学报(自然科学学报), 3, 1-3.
[6] 赵燕 (2005) 完全图与完全二部图上的H-Hopf代数结构. 曲阜师范大学学报(自然科学版), 3, 25-29.
[7] 江妙浩, 任北上, 赵汝菊 (2015) 平面二元树族上的H-Hopf模结构. 广西师范院学报(自然科学学报), 3, 21-23.
[8] Dascalescu, S., Nastasescu, C. and Raianu, S. (2000) Hopf algebra: An introduction. CRC Press, Boca Raton.
[9] Brouder, Ch. (2000) On the trees of quantum fields. The European Physical Journal C, 12, 535-549.
[10] Grossman, R. and Larson, R.G. (1989) Hopf algebraic structure of families of trees. Journal of Algebra, 126, 184-210.
[11] Brouder, Ch. and Frabetti, A. (2001) Renormalization of QED with planar binary trees. European Physical Journal C, 19, 715-741.
[12] Brouder, Ch. and Frabetti, A. (2003) QED Hopf algebra on planar binary trees. Journal of Algebra, 267, 298-322.
[13] Connes, A. and Kreimer, D. (2000) Renormalization in quantum field theory and the Riemann-Hilbert problem I: The Hopf algebra structure of graphs and the main theorem. Communications in Mathematical Physics, 210, 249-273.
[14] Molnar, R.K. (1977) Semi-direct products of Hopf algebras. Journal of Algebra, 47, 29-51.
[15] Itzykson, C. and Zuber, J.B. (1980) Quantum field theory. McGraw-Hill, New York.
[16] Loday, J.L. (2002) Arithmetree. Journal of Algebra, 258, 275-309.
[17] Kreimer, D. (1998) On the Hopf algebra structure of perturbative quantum field theories. Advances in Theoretical and Mathematical Physics, 2, 303-334.
[18] Loday, J.L. and Ronco, M.O. (1998) Hopf algebra of the planar binary trees. Advances in Mathematics, 139, 293-309.
[19] Foissy, L. (2002) Les algèbres de Hopf des arbres enracinés décorés I. Bulletin des Sciences Mathématiques, 126, 193- 239.
[20] Holtkamp, R. (2003) Comparison of Hopf algebras on trees. Archiv der Mathematik, 80, 368-383.
[21] Loday, J.L. and Ronco, M.O. Order structure on the algebra of permutations and planar binary trees. Journal of Algebraic Combinatorics, to Appear.
[22] Peskin, M.E. and Schroeder, D.V. (1995) An introduction to quantum field theory. Perseus Books Pub. L.L.C., New York.