Yang-Mills Theories in Axial and Light-Cone Gauges, Analytic Regularization and Ward Identities

李弘謙(H. C. Lee)

Chinese Journal of Physics

23卷2期（1985 / 07 / 01）

90 - 143

英文

The application of the principles of generalization and analytic continuation to the regularization of divergent Feynman integrals is discussed. The technique, or analytic regularization, which is a generalization of dimensional regularization, is used to derive analytic representations for two classes of massless two-point integrals. The first class is based on the principal-value prescription and includes integrals encountered in quantum field theories in the ghost-free axial gauge (n．A = 0), reducing in a special case to integrals in the light-cone gauge (n．A = 0, n^2 = 0). The second class is based on the Mandelstam prescription devised especially for the light-cone gauge. For some light-cone gauge integrals the two representations are not equivalent. Both classes include as a sub-class integrals in the Lorentz covariant ”&gauges”. The representations are used to compute one-loop corrections to the self-energy and the three-vertex in Yang-Mills theories in the axial and light-cone gauges, showing that the two-, and three-point Ward identities are satisfied; to illustrate that ultraviolet and infrared singularities, indistinguishable in dimensional regularization, can be separated analytically; and to show that certain tadpole integrals vanish only because of an exact cancellation between ultraviolet and infrared singularities. In the axial gauge, the wavefunction and vertex renormalization constants, Z3 and Z1, are identical, so that the o-function can be directly derived from Z3 (i.e. from the self-energy), the result being the same as that computed in the covariant E-gauges. Preliminary results suggest that the light-cone gauge in the Mandelstam prescription, but not in the principal value prescription, has the same renormalization property of the axial gauge.