Abstract
In the literature one can find two different expressions for the gauge-field propagator in light-cone gauge, containing the sum of three rather than two terms. The question of which of the two is the correct one has been a subject of debate. We propose a solution to this question by evaluating one-loop level processes in QED, both in the covariant approach in the light-cone gauge and in the light-front time-ordered perturbation theory (TOPT) approach, proving the equivalence between the two formulations of the theory. The form of the propagator turns out to be crucial in the proof, in particular as concerns its relation with the diagrams containing instantaneously propagating photons and instantaneous interactions. We show that the diagrams in light-front TOPT with instantaneous photons can be recovered in the covariant approach starting from the propagators with only two terms. Our proof of the equivalence clarifies which form should be used for the gauge-field propagator in the covariant approach. This result naturally applies to the QCD case also.
Similar content being viewed by others
References
M. Sawicki, Light front limit in a rest frame. Phys. Rev. D 44, 433–440 (1991)
C. Ji, Z. Li, A.T. Suzuki, Electromagnetic gauge field interpolation between the instant form and the front form of the Hamiltonian dynamics. Phys. Rev D 91, 065020 (2014)
A. Misra, S. Warawdekar, Equivalence of covariant and light front QED at one loop level. Phys. Rev. D 71, 125011 (2005)
P.P. Srivastava, S.J. Brodsky, Light front quantized QCD in light cone gauge. Phys. Rev. D 64, 045006 (2000)
A.T. Suzuki, J.H.O. Sales: Light front gauge propagator reexamined (2003). arXiv:hep-th/0304065
Mantovani, L., Pasquini, B., Xiong, X., Bacchetta, A.: Revisiting the equivalence of light-front and covariant QED in the light-cone gauge. Phys. Rev. D 94, 116005 (2016). doi:10.1103/PhysRevD.94.116005
D. Mustaki, S. Pinsky, J. Shigemitsu, K. Wilson, Perturbative renormalization of null plane QED. Phys. Rev. D 43, 3411–3427 (1991)
Author information
Authors and Affiliations
Corresponding author
Additional information
This research has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant Agreement Nos. 647981, 3DSPIN). This work was supported through the McCartor Fund Fellowship program under the auspices of International Light-Cone Advisory Committee (ILCAC).
This article belongs to the Topical Collection “Light Cone 2016”.
Rights and permissions
About this article
Cite this article
Mantovani, L., Bacchetta, A., Pasquini, B. et al. The Gauge-Field Propagator in Light-Cone Gauge: Which is the Correct One?. Few-Body Syst 58, 84 (2017). https://doi.org/10.1007/s00601-017-1237-y
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s00601-017-1237-y