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依据定量因果原理,给出了物理学中的一个因果代数的应用,当满足定量因果原理的互逆可消条件且又满足消去律的解时, 得到因果分解代数;由因果分解代数导出了结合律和单位元,进而导出了因果分解代数又具有群的结构特征,同时给出了这新代数系统在高能物理学中的应用.严格地给出了在高能物理中既不是群又不是环的反应,发现因果代数和因果分解代数是严格描述粒子物理反应的基本工具,得到了所有各种相加性、相乘性物理量和各种粒子反应都必须满足的统一恒等式,给出了因果代数和因果分解代数对高能物理的具体应用.利用因果代数的表示和超对称的R数,得到了含有超对称粒子反应中相乘性的超对称的PR=(-1)R对称性.还得到了一个关于电子自旋角动量的任意分量间的一个对称关系式,利用这对称关系式,可以化简多电子相互作用的计算.利用互逆可消条件定义了一般的逆元,可重新定义群,使群的公理减少一个,消除了重复定义.A causal algebra and its application to high energy physics is proposed. Firstly on the basis of quantitative causal principle, we propose both a causal algebra and a causal decomposition algebra. Using the causal decomposition algebra, the associative law and the identity are deduced, and it is inferred that the causal decomposition algebra naturally contains the structures of group. Furthermore, the applications of the new algebraic systems are given in high energy physics. We find that the reactions of particles of high energy belonging neither to the group nor to the ring, and the causal algebra and the causal decomposition algebra are rigorous tools exactly describing real reactions of particle physics. A general unified expression (with multiplicative or additive property) of different quantities of interactions between different particles is obtained. Using the representation of the causal algebra and supersymmetric R number, the supersymmetric PR=(-1 )R invariance of multiplying property in the reactions of containing supersymmetric particles is obtained. Furthermore, a symmetric relation between any components of electronic spin is obtained, with the help of which one can simplify the calculation of interactions of many electrons. The reciprocal eliminable condition to define general inverse elements is used, which may renew the definition of the group and make the number of axioms of group reduced to three by eliminating a superabundant definition.
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Keywords:
- symmetry /
- group theory /
- causal principle /
- particle physics
[1] Cornwell J A 1984 Group Theory In Physics (Vol.Ⅰ,Ⅱ) (London: Academic Press)
[2] Huang Y C, Lee X G, Shao M X 2006 Mod. Phys. Lett. A 21 1107
[3] Huang Y C, Weng G 2005 Commun. Theor. Phys. 44 757
[4] Huang Y C, Lin B L 2002 Phys. Lett. A 299 644
[5] Huang Y C, Yu C X 2007 Phys. Rev. D 75 044011
[6] Xiong Q Y 1994 Modern Algebra (Wuhan: Wuhan University Press)
[7] Sholander M 1959 Am. Math. Month. 66 93
[8] Michel S, Single A 1961 Am. Math. Month. 68 346
[9] Burris S, Sankappanavar H P 1981 A Course in Universal Algebra (Berlin: Springer-Verlag)
[10] Kobayashi S, Nomizu K 1969 Foundations of Differential Geometry (Vol.Ⅰ,Ⅱ.) (Tokyo: Interscience)
[11] Husemoller D 1975 Fibre Bundles (Berlin: Springer-Verlag)
[12] Nash C, Sen S 1983 Topology and Geometry for Physicists (London: Academic Press)
[13] Chern S S 1988 Vector Bundles With a Connection, Studies in Global Differential Geometry, Mathematical Association of America.
[14] Yang S L 1998 Algebra Colloquium 5 459
[15] Xiao J, Yang S L 2001 Algebras and Representation Theory 4 491
[16] Otto Nachtmann 1990 Elementary Particle Physics—Concepts and Phenomena (Translated by A. Lahee and W. Wetzel, Berlin: Springer-Verlag)
[17] Kolb E W, Turner M S 1990 The Early Universe (New York: Addison-Wesley Publishing Company)
[18] Linde A D 1990 Particle Physics and Inflationary Cosmology (Berkshire: Harwood Academic publishers)
[19] Llewellyn Smith C H 1982 Physics Reports 24 1
[20] Sergio Ferrara 1987 Supersymmetry (Amsterdam: Elsevier Science Pub. Co.)
[21] Polchinski J 1998 String Theory, Vol.Ⅰ, Ⅱ (New York: Cambridge University Press);Davies P C W, Brown J 1988 Superstrings (Cambridge:Cambridge University Press)
[22] Green M B, Schwarz J H, Witten E 1988 Superstring Theory (Cambridge: Cambridge University Press)
[23] Dong W S, Huang B X 2010 Acta Phys. Sin. 59 1 (in Chinese) [董文山、黄宝歆 2010 59 1]
[24] Jia L Q, Cui J C, Zhang Y Y, Luo S K 2009 Acta Phys. Sin. 58 16 (in Chinese) [崔金超、贾利群、罗绍凯、张耀宇 2009 58 16]
[25] Fang J H, Liu Y K 2008 Acta Phys. Sin. 57 6699 (in Chinese) [方建会、刘仰魁 2008 57 6699]
[26] Wang C, Zhang K, Zhou L B 2008 Acta Phys. Sin. 57 6718 (in Chinese) [王 策、张 凯、周利斌 2008 57 6718]
[27] Zhang Y 2009 Chin. Phys. B 18 4636
[28] Lin P, Fang J, Pang T 2008 Chin. Phys. B 17 4361
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[1] Cornwell J A 1984 Group Theory In Physics (Vol.Ⅰ,Ⅱ) (London: Academic Press)
[2] Huang Y C, Lee X G, Shao M X 2006 Mod. Phys. Lett. A 21 1107
[3] Huang Y C, Weng G 2005 Commun. Theor. Phys. 44 757
[4] Huang Y C, Lin B L 2002 Phys. Lett. A 299 644
[5] Huang Y C, Yu C X 2007 Phys. Rev. D 75 044011
[6] Xiong Q Y 1994 Modern Algebra (Wuhan: Wuhan University Press)
[7] Sholander M 1959 Am. Math. Month. 66 93
[8] Michel S, Single A 1961 Am. Math. Month. 68 346
[9] Burris S, Sankappanavar H P 1981 A Course in Universal Algebra (Berlin: Springer-Verlag)
[10] Kobayashi S, Nomizu K 1969 Foundations of Differential Geometry (Vol.Ⅰ,Ⅱ.) (Tokyo: Interscience)
[11] Husemoller D 1975 Fibre Bundles (Berlin: Springer-Verlag)
[12] Nash C, Sen S 1983 Topology and Geometry for Physicists (London: Academic Press)
[13] Chern S S 1988 Vector Bundles With a Connection, Studies in Global Differential Geometry, Mathematical Association of America.
[14] Yang S L 1998 Algebra Colloquium 5 459
[15] Xiao J, Yang S L 2001 Algebras and Representation Theory 4 491
[16] Otto Nachtmann 1990 Elementary Particle Physics—Concepts and Phenomena (Translated by A. Lahee and W. Wetzel, Berlin: Springer-Verlag)
[17] Kolb E W, Turner M S 1990 The Early Universe (New York: Addison-Wesley Publishing Company)
[18] Linde A D 1990 Particle Physics and Inflationary Cosmology (Berkshire: Harwood Academic publishers)
[19] Llewellyn Smith C H 1982 Physics Reports 24 1
[20] Sergio Ferrara 1987 Supersymmetry (Amsterdam: Elsevier Science Pub. Co.)
[21] Polchinski J 1998 String Theory, Vol.Ⅰ, Ⅱ (New York: Cambridge University Press);Davies P C W, Brown J 1988 Superstrings (Cambridge:Cambridge University Press)
[22] Green M B, Schwarz J H, Witten E 1988 Superstring Theory (Cambridge: Cambridge University Press)
[23] Dong W S, Huang B X 2010 Acta Phys. Sin. 59 1 (in Chinese) [董文山、黄宝歆 2010 59 1]
[24] Jia L Q, Cui J C, Zhang Y Y, Luo S K 2009 Acta Phys. Sin. 58 16 (in Chinese) [崔金超、贾利群、罗绍凯、张耀宇 2009 58 16]
[25] Fang J H, Liu Y K 2008 Acta Phys. Sin. 57 6699 (in Chinese) [方建会、刘仰魁 2008 57 6699]
[26] Wang C, Zhang K, Zhou L B 2008 Acta Phys. Sin. 57 6718 (in Chinese) [王 策、张 凯、周利斌 2008 57 6718]
[27] Zhang Y 2009 Chin. Phys. B 18 4636
[28] Lin P, Fang J, Pang T 2008 Chin. Phys. B 17 4361
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