Topological approach to examine the singularity of the axial-vector current in an Abelian gauge field theory (QED)

BAO Ai-Dong; YAO Hai-Bo; WU Shi-Shu

doi:10.1088/1674-1137/33/3/003

Chinese Physics C> 2009, Vol. 33> Issue(3) : 177-180 DOI: 10.1088/1674-1137/33/3/003

Topological approach to examine the singularity of the axial-vector current in an Abelian gauge field theory (QED)

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Abstract：
A topological way to distinguish divergences of the Abelian axial-vector current in quantum field theory is proposed. By using the properties of the Atiyah-Singer index theorem, the non-trivial Jacobian factor of the integration measure in the path-integral formulation of the theory is connected with the topological properties of the gauge field. The singularity of the fermion current related to the topological character can be correctly examined in a gauge background.

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[1]

Bertlmann R A. Anomalies. Quantum Field Theory. New York: Oxford University Press, 19962 Fujikawa K. Phys. ReV. Lett., 1979, 42: 1195; Einhorn M B, Jones D R T. Phys. Rev. D, 1984, 29: 3313 Atiyah M F, Singer I M. Ann. Math., 1971, 93: 119; Atiyah M F, Bott R, Patodi V. Invert. Math., 1973, 19: 279 4 Weinberg S. The Quantum Theory of Fields(II). Cam-bridge: Cambridge University Press, 20015 BAO A D, WU S S. Inte. Jour. Theo. Phys., 2007, 46: 12; Bardeen W. Phys. Rev., 1969, 184: 4846 Ticciati R. Quantum Field Theory for Mathematicians. Cambridge: Cambridge University Press, 19997 CHOU K C, GUO J Y, WU K. Phys. Lett. B, 1984, 134: 678 Bick E, Ste en F D. Topology and Geometry in Physics. Berlin: Springer-Verlag, 20059 YONG B L. Introduction to Quantum Field Theory. Bei-jing: Science Press, 198710 Schwinger J. Phys. Rev. Lett., 1959, 3: 296; Jackiw R, Johson K. Phys Rev., 1969, 182: 145711 SU Jun-Chen, J. Phys. G: Nucl. Part. Phys., 2004, 30: 130912 Wess J, Zumino B. Phys. Lett. B, 1971, 37: 95; Witten E. Nucl. Phys. B, 1983, 223: 422

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BAO Ai-Dong, YAO Hai-Bo and WU Shi-Shu. Topological approach to examine the singularity of the axial-vector current in an Abelian gauge field theory (QED)[J]. Chinese Physics C, 2009, 33(3): 177-180. doi: 10.1088/1674-1137/33/3/003

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Received: 2008-06-02
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通讯作者: 陈斌, bchen63@163.com

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沈阳化工大学材料科学与工程学院沈阳 110142

Topological approach to examine the singularity of the axial-vector current in an Abelian gauge field theory (QED)

Corresponding author: BAO Ai-Dong,

Received Date: 2008-06-02

Accepted Date: 2008-11-02

Available Online: 2009-03-05

Abstract:

A topological way to distinguish divergences of the Abelian axial-vector current in quantum field theory is proposed. By using the properties of the Atiyah-Singer index theorem, the non-trivial Jacobian factor of the integration measure in the path-integral formulation of the theory is connected with the topological properties of the gauge field. The singularity of the fermion current related to the topological character can be correctly examined in a gauge background.

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Topological approach to examine the singularity of the axial-vector current in an Abelian gauge field theory (QED)

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通讯作者: 陈斌, bchen63@163.com

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