Consistency of loop regularization method and divergence structure of QFTs Beyond one-loop order

  • Da HuangEmail author
  • Ling-Fong Li
  • Yue-Liang Wu
Regular Article - Theoretical Physics


We study the problem how to deal with tensor-type two-loop integrals in the Loop Regularization (LORE) scheme. We use the two-loop photon vacuum polarization in the massless Quantum Electrodynamics (QED) as the example to present the general procedure. In the processes, we find a new divergence structure: the regulated result for each two-loop diagram contains a gauge-violating quadratic harmful divergent term even combined with their corresponding counterterm insertion diagrams. Only when we sum up over all the relevant diagrams do these quadratic harmful divergences cancel, recovering the gauge invariance and locality.


Gauge Invariance Vacuum Polarization Loop Momentum Feynman Parameter General Gauge Theory 
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The authors would like to thank Jianwei Cui, Yibo Yang and Yong Tang for useful discussions. This work was supported in part by the National Science Foundation of China (NSFC) under Grant #No. 10821504, 10975170 and the Project of Knowledge Innovation Program (PKIP) of the Chinese Academy of Science.


  1. 1.
    D. Huang, Y.-L. Wu, Eur. Phys. J. C 72, 2066 (2012). arXiv:1108.3603 [hep-ph] ADSCrossRefGoogle Scholar
  2. 2.
    G. ’t Hooft, M.J.G. Veltman, Nucl. Phys. B 44, 189 (1972) ADSCrossRefGoogle Scholar
  3. 3.
    Y.L. Wu, Int. J. Mod. Phys. A 18, 5363 (2003). arXiv:hep-th/0209021 ADSCrossRefzbMATHGoogle Scholar
  4. 4.
    Y.L. Wu, Mod. Phys. Lett. A 19, 2191 (2004). arXiv:hep-th/0311082 ADSCrossRefzbMATHGoogle Scholar
  5. 5.
    J. Bjorken, S. Drell, Quantum Field Theory (McGraw-Hill, New York, 1965). 396 p. Google Scholar
  6. 6.
    M.E. Peskin, D.V. Schroeder, Introduction to Quantum Field Theory (Addison-Wesley, Reading, 1995). 842 p. Google Scholar
  7. 7.
    C. Itzykson, J.B. Zuber, Quantum Field Theory. International Series in Pure and Applied Physics (McGraw-Hill, New York, 1980). 705 p. Google Scholar
  8. 8.
    R. Jost, J.M. Luttinger, Helv. Phys. Acta 23, 201 (1950) MathSciNetzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg and Società Italiana di Fisica 2013

Authors and Affiliations

  1. 1.Kavli Institute for Theoretical Physics China (KITPC) at the CAS, State Key Laboratory of Theoretical Physics (SKLTP), Institute of Theoretical PhysicsChinese Academy of ScienceBeijingChina
  2. 2.University of Chinese Academy of SciencesBeijingChina
  3. 3.Department of PhysicsCarnegie Mellon UniversityPittsburghUSA

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