Path-Integral Derivation of the Transverse Axial Vector and Vector Anomalies in QED

Abstract

It is shown that a novel anomaly associated with transverse Ward-Takahashi identity of axial vector current in QED is derived by using Fujikawa’s method in the path-integral formulation of quantum field theory. Also it is verified that there is no transverse anomaly for the vector current.

Share and Cite:

D. Wang and A. Bao, "Path-Integral Derivation of the Transverse Axial Vector and Vector Anomalies in QED," Journal of Modern Physics, Vol. 4 No. 1, 2013, pp. 35-38. doi: 10.4236/jmp.2013.41007.

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1] Y. Takahashi, “Point Spoitting Technique and Canonical Formalism,” In: F. Mancini, Ed., Quantum Field Theory, Elsevier Science Publishers, Amsterdam, 1986, p. 19.
[2] K.-I. Kondo and Maris, “Spontaneous Chiral-Symmetry Breaking in Three-dimensional QED with a Chern-Simons Term,” Physical Review D, Vol. 52, No. 2, 1995, pp. 1212-1233. doi:10.1103/PhysRevD.52.1212
[3] H. X. He, F. C. Khanna and Y. Takahashi, “Transverse Ward-Takahashi Identity for the Fermion-Boson Vertex in Gauge Theories,” Physical Review B, Vol. 480, No. 1-2, 2000, pp. 222-228. doi:10.1016/S0370-2693(00)00353-1
[4] M. R. Pennnington and R. Williams, “Checking the Tranverse Ward-Takahashi Relation at One-loop Order in Four Dimensions,” Journal of Physics G: Nuclear and Particle Physics, Vol. 32, No. 11, 2006, p. 2219. doi:10.1088/0954-3899/32/11/014
[5] H. X. He, “Quantum Anomaly on the Transverse Ward-Takahashi Relation for the Axial-Vector Vertex,” Physical Review B, Vol. 507, No. 1-4, 2001, pp. 351-355. doi:10.1016/S0370-2693(01)00430-0
[6] W. S. Sun, H. S. Zong, X. S. Chen, et al., “A Note on Transverse Axial Vector and Vector Anomalies,” Physics Letters B, Vol. 569, No. 2, 2003, pp. 211-238. doi:10.1016/j.physletb.2003.07.033
[7] A. D. Bao and S. S. Wu, “Various Full Green Functions in QED,” International Journal of Theoretical Physics, Vol. 46, No. 12, 2007, pp. 3093-3108. doi:10.1007/s10773-007-9423-1
[8] A. D. Bao, H. B. Yao and S. S. Wu, “Topological Approach to Examine the Singularity of the Axial-Vector Currnet in an Abelian Gauge Field Theory (QED),” Chinese Physics C, Vol. 33, No. 3, 2009, p. 177. doi:10.1088/1674-1137/33/3/003
[9] H. X. He, “An Introduction to Nuclear Chromodynamics,” China University of Science and Technology Press, Hefei, 2009.
[10] H. X. He, “Transverse Ward-Takahashi Relation for the Fermion-Boson Vertex Function in Four-Dimensional Abelian Gauge theory,” International Journal of Modern Physics A, Vol. 22, No. 11, 2007, pp. 2119-2132.
[11] K. Fujikawa, “Path-Integral Measure for Gauge Invariant Field Theories,” Physical Review Letters, Vol. 42, No. 18, 1979, pp. 1195-1198.
[12] M. B. Einhorn and T. Jones, “Comment on Fujikawa’s Path-Integual Derivation of the Chiral Anomaly,” Physical Review D, Vol. 29, No. 2, 1984, pp. 331-333. doi:10.1103/PhysRevD.29.331
[13] M. Umezawa, “Regularization of the Pth-Integral Measure for Anomalies,” Physical Review D, Vol. 39, No. 12, 1989, pp. 3672-3683.

Copyright © 2024 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.