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Prog. Theor. Phys. Vol. 55 No. 3 (1976) pp. 876-888
Dispersion Calculation of the S-Matrix in Gauge Theories
Kazuo Fujikawa and
Ilham Zurayk*
Institute for Nuclear Study, University of Tokyo, Tanashi, Tokyo 188
*Department of Physics, American University of Beirut, Beirut, Lebanon
(Received August 30, 1975)
Abstract:
We study the gauge independence of dispersion relations based on the special properties of the Feynman gauge and its non-linear variants in spontaneously broken gauge theory. It is shown that the discontinuity associated with the leading singularity of a Feynman diagram has a gauge independent meaning. In particular the double spectral function associated with each box diagram is gauge independent, and this property provides a gauge independent basis for writing the Mandelstam representation for four-point functions. We also study how to fix induced vertex terms such as the muon anomalous magnetic moment in the dispersion approach. It is indicated that we can treat the finite renormalization factors in analogy with the determination of the induced terms. We then attempt to understand the renormalization program of the gauge theory as a self-consistent dispersion calculation of the S-matrix without recourse to the Ward identity. We briefly sketch how this program proceeds in the one-loop level calculation.
URL :
http://ptp.ipap.jp/link?PTP/55/876/
DOI : 10.1143/PTP.55.876
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