[1] Zhou Yuqing,. Dynamical chiral symmetry breaking in QED3 [J]. Journal of Southeast University (English Edition), 2014, 30 (4): 544-549. [doi:10.3969/j.issn.1003-7985.2014.04.024]

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Dynamical chiral symmetry breaking in QED₃()

三维QED中的动力学手征对称破缺

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Journal of Southeast University (English Edition)[ISSN:1003-7985/CN:32-1325/N]

Volumn:

30

Issue:

2014 4

Page:

544-549

Research Field:

Mathematics, Physics, Mechanics

Publishing date:

2014-12-31

Info

Title:

Dynamical chiral symmetry breaking in QED₃

三维QED中的动力学手征对称破缺

Author(s):

Zhou Yuqing

Department of Physics, Southeast University, Nanjing 211189, China

周雨青

东南大学物理系, 南京 211189

Keywords:

propagator;  covariant gauge;  3D quantum electrodynamics(QED);  equivalent pressure difference;  fermion condensation;  chiral phase transition

传播子;  协变规范;  三维QED;  等效压力差;  费米凝聚;  手征相变

PACS:

O572.24;O413.2

DOI:

10.3969/j.issn.1003-7985.2014.04.024

Abstract:

In order to examine how a propagator behaves in non-perturbative theories and how its behavior is influenced by the choice of a covariant gauge, a truncated Dyson-Schwinger equation is used to numerically investigate the properties of fermions and bosons in 3D quantum electrodynamics(QED), and a series of self-consistent solutions for the fermion propagator in the Nambu and Wigner phases are obtained. These numerical solutions show that the propagator behaves very differently in the Landau gauge domain and in the infrared energy region outside it. By using the propagators in the Nambu and Wigner phases under various gauges, it is further investigated how the fermion equivalent pressure difference and fermion condensation change with the gauge parameters. These results indicate that the phase transition described by the CJT equivalent potential and the chiral phase transition described by the chiral condensation are not completely identical.

为了研究非微扰理论中的传播子行为, 以及协变规范对其行为的影响, 以常用的截断方案下的Dyson-Schwinger方程为基础, 采用数值联立求解的方法研究了三维量子电动力学(QED)中的费米子和玻色子的行为, 并获得了一系列不同规范下费米传播子在Nambu和Wigner相中的自洽解.对这些数值解的分析表明, 远离Landau规范的红外区处, 传播子行为明显不同于Landau规范中的行为.基于Nambu和Wigner相中的不同规范下的传播子, 进一步对等效压力差和费米凝聚随规范参数的变化做了比较, 结果表明, 采用CJT等效势描述的相变与手征凝聚描述的手征相变两者之间不完全自洽.

References:

[1] Appelquis T, Nash D, Wijewardhana L C R. Critical-behavior in(2+1)-dimensional QED[J]. Physical Review Letters, 1988, 60(25): 2575-2578.
[2] Nash D. Higher-order corrections in(2+1)-dimensional QED[J]. Physical Review Letters, 1989, 62(26): 3024-3026.
[3] Maris P. Influence of the full vertex and vacuum polarization on the fermion propagator in(2+1)-dimensional QED[J]. Physical Review D, 1996, 54(6): 4049-4058.
[4] Burden C J, Roberts C D. Light-cone regular vertex in 3-dimensional quenched QED [J]. Physical Review D, 1991, 44(2): 540-550.
[5] Pisarski R D. Chiral-symmetry breaking in 3-dimensional electrodynamics[J]. Physical Review D, 1984, 29(10): 2423-2426.
[6] Appelquist T W, Bowick M, Karabali D, et al. Spontaneous chiral-symmetry breaking in 3-dimensional QED[J]. Physical Review D, 1986, 33(12): 3704-3713.
[7] Atkinson D, Johnson P W, Maris P. Dynamic mass generation in 3-dimensional QED-improved vertex function[J]. Physical Review D, 1990, 42S(2): 602-609.
[8] Curtis D C, Pennington M, Walsh D. Dynamics mass generation in QED₃ and the 1/N expansion[J]. Physics Letters B, 1992, 295(3/4):313-319.
[9] Kondo K, Nakatani H. Cutoff dependence of self-consistent solutions in unquenched QED₃[J]. Progress of Theoretical Physics, 1992, 87(1):193-206.
[10] Bashir A, Raya A. Landau-Khalatnikov-Fradkin transformations and the fermion propagator in quantum electrodynamics[J]. Physical Review D, 2002, 66(10):105005.
[11] Bashir A. Non-perturbative fermion propagator for the massless quenched QED₃[J]. Physics Letters B, 2000, 491(3/4):280-284.
[12] Liu G Z, Cheng G. Effect of gauge boson mass on chiral symmetry breaking in three-dimensional QED[J]. Physical Review D, 2003, 67(6), 065010.
[13] Feng H T, Sun W M, Hu F, et al. The influence of the gauge boson mass on the critical number of the fermion flavors in QED(3)[J]. International Journal of Modern Physics A, 2005, 20(13):2753-2762.
[14] Burden C J, Praschifka J, Roberts C D. Photon polarization tensor and gauge dependence in 3-dimensional quantum electrodynamics[J]. Physical Review D, 1992, 46(6):2695-2702.
[15] Maris P. Confinement and complex singularities in 3-dimensional QED[J]. Physical Review D, 1995, 52(10): 6087-6097.
[16] Herbut I F, Seradjeh B H. Permanent confinement in the compact QED₃ with fermionic matter[J]. Physical Review Letters, 2003, 91(17):171601.
[17] Burden C J, Praschifka J, Roberts C D. Photon polarization tensor and gauge dependence in 3-dimensional quantum electrodynamics[J]. Physical Review D, 1992, 46(6): 2695-2702.
[18] Fischer C S, Alkofer R, Dahm T, et al. Dynamical chiral symmetry breaking in unquenched QED₃[J]. Physical Review D, 2004, 70(7):073007.
[19] Simmons E H. Useful gauges for studying dynamic fermion mass generation in arbitrary space-time dimension[J]. Physical Review D, 1990, 42(8): 2933-2935.
[20] Kondo K I, Maris P. First-order phase-transition in 3-dimensional QFD with chern-simons term[J]. Physical Review Letters, 1995, 74(1):18-21.
[21] Gusynin V P, Hams A H, Reenders M.(2+1)-dimensional QED with dynamically massive fermions in vacuum polarization[J]. Physical Review D, 1996, 53(4):2227-2235.
[22] King J E. Transverse vertex and gauge technique in quantum electrodynamics[J]. Physical Review D, 1983, 27(8):1821-1829.
[23] Curtis D C, Pennington M R. Truncating the Schwinger-Dyson equations: how multiplicative renormalizability and the ward identity restrict the 3-point vertex in QED[J]. Physical Review D, 1990, 42(12): 4165-4169.
[24] Ball J S, Chiu T W. Analytic properties of the vertex function in gauge-theories.I [J]. Physical Review D, 1980, 22(10): 2542-2549.
[25] Haymaker R W. Variational-methods for composite-operators[J]. Rivista del Nuovo Cimento, 1991, 14(8):1-89.
[26] Burden C J, Roberts C D. Gauge covariance and the fermion-photon vertex in 3-dimensional and 4-dimensional, massless quantum electrodynamics[J]. Physical Review D, 1993, 47(12):5581-5588.
[27] Stam K. Dynamical chiral symmetry-breaking[J]. Physics Letters B, 1985, 152(3/4): 238-240.
[28] Cornwall J M, Jackiw R, Tomboulis E. Effective action for composite operators[J]. Physical Review D, 1974, 10(8):2428-2445.

Memo

Memo:

Biography: Zhou Yuqing(1961—), male, doctor, professor, zhou_-yuqing@263.net.
Foundation items: The National Natural Science Foundation of China(No.10947127), the Science Foundation of Southeast University(No.11047005),
Citation: Zhou Yuqing.Dynamical chiral symmetry breaking in QED₃[J].Journal of Southeast University(English Edition), 2014, 30(4):544-549.[doi:10.3969/j.issn.1003-7985.2014.04.024]

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