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General theory of renormalization of gauge theories in nonlinear gauges

Authors:	Satish D Joglekar

Institution:	(1) Department of Physics, Indian Institute of Technology, 208016 Kanpur, India

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.

Keywords:	Gauge theory renormalization nonlinear gauge
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