General theory of renormalization of gauge theories in nonlinear gauges

Abstract

We discuss the general theory of renormalization of unbroken gauge theories in the nonlinear gauges in which the gauge-fixing term is of the form$- \frac{1}{2}\sum\limits_\alpha {f_\alpha ^2 [A] = - \frac{1}{2}} \sum\limits_\alpha {\frac{1}{{\eta _\alpha }}(\partial ^\mu A_\mu ^\alpha + \zeta _{\beta \gamma }^\alpha A_\mu ^\beta A^{\gamma \mu } )^2 }$ We show that higher loop renormalization modifiesfα [A] to contain ghost terms of the form$f_\alpha [A,c,\bar c] = \eta _\alpha ^{ - \frac{1}{2}} (\partial ^\mu A_\mu ^\alpha + \zeta _{\beta \gamma }^\alpha A_\mu ^\beta A^{\gamma \mu } + \tau _\gamma ^{\alpha \beta } \bar c_\beta c_\gamma )$ and show how the corresponding ghost terms are deduced fromfα [A, c, c] uniquely. We show that the theory can be renormalized while preserving a modified form of BRS invariance by multiplicative and independent renormalizations onA, c, g, η, ζ, τ. We briefly discuss the independence of the renormalized S-matrix from η,ζ, τ.