Non-Abelian chiral kinetic equations in the Cartan-Weyl basis

Luo Xiao-Li; Gao Jian-Hua

doi:10.7498/aps.72.20222471

Abstract

Non-Abelian gauge field is the fundamental element of the standard model. Non-Abelian chiral kinetic theory can be used to describe how the chiral fermions in standard model transport in a non-equilibrium system. In our previous work, we decomposed the non-Abelian chiral kinetic equations into color singlet and multiplet in the $SU(N)$ color space. In this formalism, the chiral kinetic equations preserve the gauge symmetry in a very apparent way. However, sometimes we need to describe the microscopic process of the specific color degree, e.g. the color connection in the hadronization stage. In order to describe such a process, it will be more convenient to decompose the non-Abelian chiral kinetic equations in the Cartan-Weyl basis. In this work, we choose the matrix elements of the Wigner function in fundamental representation of color space as the direct variables and decompose the gauge field or strength tensor field in the Cartan-Weyl basis. By using the covariant gradient expansion, we decompose the non-Abelian chiral kinetic equations into the coupled kinetic equations for diagonal distribution function and non-diagonal distribution function up to the first order. When only diagonal elements exist in the gauge field with non-diagonal elements and diagonal elements decoupled, the non-Ableian chiral kinetic equation will be reduced to the form in the Abelian case. When the non-diagonal elements of the gauge field are present, the kinetic equations are totally tangled between diagonal distribution function and non-diagonal distribution function. Especially, the $0$th-order non-diagonal distribution function could induce the $1$st-order diagonal Wigner function, and the $0$th-order diagonal distribution function could also induce the $1$st-order non-diagonal Wigner function.

Keywords:

Authors and contacts

Shandong Provincial Key Laboratory of Optical Astronomy and Solar-Terrestrial Environment, School of Space Science and Physics, Shandong University, Weihai 264209, China

Corresponding author: Gao Jian-Hua, gaojh@sdu.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 11890710, 11890713, 12175123)

FullText HTML : translate this paragraph

References

[1]	Vilenkin A 1980 Phys. Rev. D 22 3080 Google Scholar
[2]	Kharzeev D E, McLerran L D, Warringa H J 2008 Nucl. Phys. A 803 227 Google Scholar
[3]	Fukushima K, Kharzeev D E, Warringa H J 2008 Phys. Rev. D 78 074033 Google Scholar
[4]	Vilenkin A 1978 Phys. Lett. 80B 150
[5]	Kharzeev D, Zhitnitsky A 2007 Nucl. Phys. A 797 67 Google Scholar
[6]	Erdmenger J, Haack M, Kaminski M, Yarom A 2009 JHEP 0901 055
[7]	Banerjee N, Bhattacharya J, Bhattacharyya S, Dutta S, Loganayagam R, Surowka P 2011 JHEP 1101 094
[8]	Son D T, Zhitnitsky A R 2004 Phys. Rev. D 70 074018 Google Scholar
[9]	Metlitski M A, Zhitnitsky A R 2005 Phys. Rev. D 72 045011 Google Scholar
[10]	Gao J H, Liang Z T, Pu S, Wang Q, Wang X N 2012 Phys. Rev. Lett. 109 232301 Google Scholar
[11]	Stephanov M A, Yin Y 2012 Phys. Rev. Lett. 109 162001 Google Scholar
[12]	Son D T, Yamamoto N 2013 Phys. Rev. D 87 085016 Google Scholar
[13]	Chen J W, Pu S, Wang Q, Wang X N 2013 Phys. Rev. Lett. 110 262301 Google Scholar
[14]	Manuel C, Torres-Rincon J M 2014 Phys. Rev. D 89 096002 Google Scholar
[15]	Manuel C, Torres-Rincon J M 2014 Phys. Rev. D 90 076007 Google Scholar
[16]	Chen J Y, Son D T, Stephanov M A, Yee H U, Yin Y 2014 Phys. Rev. Lett. 113 182302 Google Scholar
[17]	Chen J Y, Son D T, Stephanov M A 2015 Phys. Rev. Lett. 115 021601 Google Scholar
[18]	Hidaka Y, Pu S, Yang D L 2017 Phys. Rev. D 95 091901 Google Scholar
[19]	Mueller N, Venugopalan R 2018 Phys. Rev. D 97 051901 Google Scholar
[20]	Huang A, Shi S, Jiang Y, Liao J, Zhuang P 2018 Phys. Rev. D 98 036010 Google Scholar
[21]	Gao J H, Liang Z T, Wang Q, Wang X N 2018 Phys. Rev. D 98 036019 Google Scholar
[22]	Liu Y C, Gao L L, Mameda K, Huang X G 2019 Phys. Rev. D 99 085014 Google Scholar
[23]	Lin S, Shukla A 2019 JHEP 6 060
[24]	Gao L L, Huang X G 2022 Chin. Phys. Lett. 39 021101 Google Scholar
[25]	Peng H H, Zhang J J, Sheng X L, Wang Q 2021 Chin. Phys. Lett. 38 116701 Google Scholar
[26]	Sun Y, Ko C M, Li F 2016 Phys. Rev. C 94 045204
[27]	Sun Y, Ko C M 2017 Phys. Rev. C 95 034909 Google Scholar
[28]	Sun Y, Ko C M 2017 Phys. Rev. C 96 024906 Google Scholar
[29]	Sun Y, Ko C M 2018 Phys. Rev. C 98 014911 Google Scholar
[30]	Sun Y, Ko C M 2019 Phys. Rev. C 99 011903 Google Scholar
[31]	Zhou W H, Xu J 2018 Phys. Rev. C 98 044904 Google Scholar
[32]	Zhou W H, Xu J 2019 Phys. Lett. B 798 134932 Google Scholar
[33]	Liu S Y F, Sun Y, Ko C M 2020 Phys. Rev. Lett. 125 062301 Google Scholar
[34]	Stone M, Dwivedi V 2013 Phys. Rev. D 88 045012 Google Scholar
[35]	Akamatsu Y, Yamamoto N 2014 Phys. Rev. D 90 125031 Google Scholar
[36]	Hayata T, Hidaka Y 2017 PTEP 2017 073I01
[37]	Mueller N, Venugopalan R 2019 Phys. Rev. D 99 056003 Google Scholar
[38]	Luo X L, Gao J H 2021 JHEP 11 115
[39]	Yang D L 2022 JHEP 06 140
[40]	Heinz U W 1983 Phys. Rev. Lett. 51 351 Google Scholar
[41]	Elze H T, Gyulassy M, Vasak D 1986 Phys. Lett. B 177 402 Google Scholar
[42]	Elze H T, Gyulassy M, Vasak D 1986 Nucl. Phys. B 276 706 Google Scholar
[43]	Elze H T, Heinz U W 1989 Phys. Rept. 183 81 Google Scholar
[44]	Ezawa Z F, Iwazaki A 1982 Phys. Rev. D 25 2681
[45]	Ezawa Z F, Iwazaki A 1982 Phys. Rev. D 26 631
[46]	Gyulassy M, Iwazaki A 1985 Phys. Lett. B 165 157 Google Scholar
[47]	Huang X G, Mitkin P, Sadofyev A F, Speranza E 2020 JHEP 10 117
[48]	Hattori K, Hidaka Y, Yamamoto N, Yang D L 2021 JHEP 2 1
[49]	Lin S 2022 Phys. Rev. D 105 076017 Google Scholar

Cited By

[1]	Vilenkin A 1980 Phys. Rev. D 22 3080 Google Scholar
[2]	Kharzeev D E, McLerran L D, Warringa H J 2008 Nucl. Phys. A 803 227 Google Scholar
[3]	Fukushima K, Kharzeev D E, Warringa H J 2008 Phys. Rev. D 78 074033 Google Scholar
[4]	Vilenkin A 1978 Phys. Lett. 80B 150
[5]	Kharzeev D, Zhitnitsky A 2007 Nucl. Phys. A 797 67 Google Scholar
[6]	Erdmenger J, Haack M, Kaminski M, Yarom A 2009 JHEP 0901 055
[7]	Banerjee N, Bhattacharya J, Bhattacharyya S, Dutta S, Loganayagam R, Surowka P 2011 JHEP 1101 094
[8]	Son D T, Zhitnitsky A R 2004 Phys. Rev. D 70 074018 Google Scholar
[9]	Metlitski M A, Zhitnitsky A R 2005 Phys. Rev. D 72 045011 Google Scholar
[10]	Gao J H, Liang Z T, Pu S, Wang Q, Wang X N 2012 Phys. Rev. Lett. 109 232301 Google Scholar
[11]	Stephanov M A, Yin Y 2012 Phys. Rev. Lett. 109 162001 Google Scholar
[12]	Son D T, Yamamoto N 2013 Phys. Rev. D 87 085016 Google Scholar
[13]	Chen J W, Pu S, Wang Q, Wang X N 2013 Phys. Rev. Lett. 110 262301 Google Scholar
[14]	Manuel C, Torres-Rincon J M 2014 Phys. Rev. D 89 096002 Google Scholar
[15]	Manuel C, Torres-Rincon J M 2014 Phys. Rev. D 90 076007 Google Scholar
[16]	Chen J Y, Son D T, Stephanov M A, Yee H U, Yin Y 2014 Phys. Rev. Lett. 113 182302 Google Scholar
[17]	Chen J Y, Son D T, Stephanov M A 2015 Phys. Rev. Lett. 115 021601 Google Scholar
[18]	Hidaka Y, Pu S, Yang D L 2017 Phys. Rev. D 95 091901 Google Scholar
[19]	Mueller N, Venugopalan R 2018 Phys. Rev. D 97 051901 Google Scholar
[20]	Huang A, Shi S, Jiang Y, Liao J, Zhuang P 2018 Phys. Rev. D 98 036010 Google Scholar
[21]	Gao J H, Liang Z T, Wang Q, Wang X N 2018 Phys. Rev. D 98 036019 Google Scholar
[22]	Liu Y C, Gao L L, Mameda K, Huang X G 2019 Phys. Rev. D 99 085014 Google Scholar
[23]	Lin S, Shukla A 2019 JHEP 6 060
[24]	Gao L L, Huang X G 2022 Chin. Phys. Lett. 39 021101 Google Scholar
[25]	Peng H H, Zhang J J, Sheng X L, Wang Q 2021 Chin. Phys. Lett. 38 116701 Google Scholar
[26]	Sun Y, Ko C M, Li F 2016 Phys. Rev. C 94 045204
[27]	Sun Y, Ko C M 2017 Phys. Rev. C 95 034909 Google Scholar
[28]	Sun Y, Ko C M 2017 Phys. Rev. C 96 024906 Google Scholar
[29]	Sun Y, Ko C M 2018 Phys. Rev. C 98 014911 Google Scholar
[30]	Sun Y, Ko C M 2019 Phys. Rev. C 99 011903 Google Scholar
[31]	Zhou W H, Xu J 2018 Phys. Rev. C 98 044904 Google Scholar
[32]	Zhou W H, Xu J 2019 Phys. Lett. B 798 134932 Google Scholar
[33]	Liu S Y F, Sun Y, Ko C M 2020 Phys. Rev. Lett. 125 062301 Google Scholar
[34]	Stone M, Dwivedi V 2013 Phys. Rev. D 88 045012 Google Scholar
[35]	Akamatsu Y, Yamamoto N 2014 Phys. Rev. D 90 125031 Google Scholar
[36]	Hayata T, Hidaka Y 2017 PTEP 2017 073I01
[37]	Mueller N, Venugopalan R 2019 Phys. Rev. D 99 056003 Google Scholar
[38]	Luo X L, Gao J H 2021 JHEP 11 115
[39]	Yang D L 2022 JHEP 06 140
[40]	Heinz U W 1983 Phys. Rev. Lett. 51 351 Google Scholar
[41]	Elze H T, Gyulassy M, Vasak D 1986 Phys. Lett. B 177 402 Google Scholar
[42]	Elze H T, Gyulassy M, Vasak D 1986 Nucl. Phys. B 276 706 Google Scholar
[43]	Elze H T, Heinz U W 1989 Phys. Rept. 183 81 Google Scholar
[44]	Ezawa Z F, Iwazaki A 1982 Phys. Rev. D 25 2681
[45]	Ezawa Z F, Iwazaki A 1982 Phys. Rev. D 26 631
[46]	Gyulassy M, Iwazaki A 1985 Phys. Lett. B 165 157 Google Scholar
[47]	Huang X G, Mitkin P, Sadofyev A F, Speranza E 2020 JHEP 10 117
[48]	Hattori K, Hidaka Y, Yamamoto N, Yang D L 2021 JHEP 2 1
[49]	Lin S 2022 Phys. Rev. D 105 076017 Google Scholar

[1]	Liu Qing-Kang, Zhang Xu, Cai Hong-Bo, Zhang En-Hao, Gao Yan-Qi, Zhu Shao-Ping. Suppression of stimulated Raman scattering kinetic bursts by intensity-modulated broadband laser. Acta Physica Sinica, 2024, 73(5): 055202. doi: 10.7498/aps.73.20231679
[2]	Zeng Chao, Mao Yi-Yi, Wu Ji-Zhou, Yuan Tao, Dai Han-Ning, Chen Yu-Ao. Topological phase in one-dimensional momentum space lattice of ultracold atoms without chiral symmetry. Acta Physica Sinica, 2024, 73(4): 040301. doi: 10.7498/aps.73.20231566
[3]	Bai Jing, Ma Wen-Hao, Ge Cheng-Xian, Wu Zhen-Sen, Xu Tong. Radiation force characteristics of non-uniform chiral stratified particles in standing wave field. Acta Physica Sinica, 2024, 73(18): 184201. doi: 10.7498/aps.73.20240842
[4]	Zhou Li-Na, Hu Han-Qing, Liu Yue-Qiang, Duan Ping, Chen Long, Zhang Han-Yu. Modelling study of fluid and kinetic responses of plasmas to resonant magnetic perturbation. Acta Physica Sinica, 2023, 72(7): 075202. doi: 10.7498/aps.72.20222196
[5]	Gao Jian-Hua, Sheng Xin-Li, Wang Qun, Zhuang Peng-Fei. Relativistic spin transport theory for spin-1/2 fermions. Acta Physica Sinica, 2023, 72(11): 112501. doi: 10.7498/aps.72.20222470
[6]	Bai Jing, Ge Cheng-Xian, He Lang, Liu Xuan, Wu Zhen-Sen. Analysis of trapping force exerted on multi-layered chiral sphere induced by laser sheet. Acta Physica Sinica, 2022, 71(10): 104208. doi: 10.7498/aps.71.20212284
[7]	Wang Jing. Chiral Majorana fermion. Acta Physica Sinica, 2020, 69(11): 117302. doi: 10.7498/aps.69.20200534
[8]	He Ying-Ping, Hong Jian-Song, Liu Xiong-Jun. Non-abelian statistics of Majorana modes and the applications to topological quantum computation. Acta Physica Sinica, 2020, 69(11): 110302. doi: 10.7498/aps.69.20200812
[9]	Yu Bo, He Qiu-Yan, Yuan Xiao. Scaling fractal-lattice franctance approximation circuits of arbitrary order and irregular lattice type scaling equation. Acta Physica Sinica, 2018, 67(7): 070202. doi: 10.7498/aps.67.20171671
[10]	Wen Yuan-Hui, Chen Yu-Jie, Yu Si-Yuan. Design of accelerating beams based on caustic method. Acta Physica Sinica, 2017, 66(14): 144210. doi: 10.7498/aps.66.144210
[11]	Guo Li, Han Shen-Sheng, Chen Jing. Study of above-threshold ionization by Wigner-distribution-like function method. Acta Physica Sinica, 2016, 65(22): 223203. doi: 10.7498/aps.65.223203
[12]	Luo Xiang-Yi, Ben Shuai, Ge Xin-Lei, Wang Qun, Guo Jing, Liu Xue-Shen. High-order harmonics and attosecond pulse generation of a He+ ion by a chirped two-color inhomogeneous laser field. Acta Physica Sinica, 2015, 64(19): 193201. doi: 10.7498/aps.64.193201
[13]	Zou Chang-Lin, Ye Wen-Hua, Lu Xin-Pei. Study of laser plasma interactions using one-dimensional particle-in-cell code in kinetic regime. Acta Physica Sinica, 2014, 63(8): 085207. doi: 10.7498/aps.63.085207
[14]	Liao Chang-Geng, Chen Zi-Hong, Luo Cheng-Li. Dynamics of Bell nonlocality in non-degenerate two-photon Jaynes-Cummings model. Acta Physica Sinica, 2010, 59(12): 8526-8534. doi: 10.7498/aps.59.8526
[15]	Hong Wei-Yi, Yang Zhen-Yu, Lan Peng-Fei, Zhang Qing-Bin, Li Qian-Guang, Lu Pei-Xiang. Generating isolated broadband attosecond pulses with stable pulse duration in a non-colinear polarized two-color field. Acta Physica Sinica, 2009, 58(7): 4914-4919. doi: 10.7498/aps.58.4914
[16]	YANG SHI-XIN. A MATHEMATICAL MODEL OF SURFACE-PRESSURE-INDUCED SEPARATION OF CHIRAL PHASES IN MONOLAYER OF RACEMIC AMPHIPHILES AND ITS CLASSICAL SOLUTIONS IN TWO-DIMENSIONAL CASE. Acta Physica Sinica, 1998, 47(10): 1673-1679. doi: 10.7498/aps.47.1673
[17]	Zhou Yun-Song, Yang Zhen, Hu Hua-Shen. . Acta Physica Sinica, 1995, 44(5): 726-733. doi: 10.7498/aps.44.726
[18]	HE XIANG-HAO, XIAN DING-CHANG. THE SCHWINGER-DYSON EQUATIONS OF THE WILSON LOOP VARIABLE IN THE LATXTICE GAUGEX FIELD THEORY AND THE PROBLEM OF UNIVERSALITY. Acta Physica Sinica, 1985, 34(7): 882-891. doi: 10.7498/aps.34.882
[19]	WANG PEI, HOU BO-YUAN, HOU BO-YU, GUO HAN-YING. DUAL SYMMETRY OF CHIRAL MODEL AND GEOMETRICAL CORRESPONDENCE BETWEEN CHIRAL FIELD AND SINE-GORDON EQUATION. Acta Physica Sinica, 1984, 33(3): 294-301. doi: 10.7498/aps.33.294
[20]	LI HUA-ZHONG, XIAN DING-CHANG, GUO SHUO-HONG. SOLITON SOLUTIONS OF NON-ABELIAN GAUGE FIELDS. Acta Physica Sinica, 1977, 26(6): 544-549. doi: 10.7498/aps.26.544

Catalog

Vol. 72, Issue 11 - 2023-06-05

Metrics

Abstract views: 2927
PDF Downloads: 71
Cited By: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

Search

Article

留言板