- Type Singularities in Axial Gauges

The axial-gauge boson propagator contains 1/(η · k) p-type singularities. These singualarities have generally been treated by inventing prescriptions for them. We propose an alternative procedere for treating these singularities in the path-integral formalism using the known way of treating the 1/k 2n-type singularities in Lorentz-type gauges. For this purpose we use a finite field-dependent BRS transformation that inerpolates between the Lorentz and axial-type gauges. We arrive at the ǫ-dependent tree propagator in axial-type gauges. Calculations in nonabelaian gauge theories require a choice of gauge. There are many families of gauges that have been used in practical calculations, e.g., Lorentz-type gauges, axial gauges. It becomes an important question as to how the calculations in various (families of) gauge choices are related to each other. Gauge-independence in a limited framework, has been proven in early days. Such proofs utililize the infinitesimal gauge transformations reponsible for gauge-parameter change. Ways of connecting Green's functions in family of gauges (and establishing expliticly gauge-independence) has not been done until recently. Discrepancies have been reported in anomalous dimension calculations in the Lorentz-type and axial-type gauges. Thus, it becomes important to obtain a procedure to connect the Green functions in different families of gauges. Unlike gauge transformations, " infinitesimal " and " finite " BRS transformations have the same form. This makes them suitable for our purpose. The FP effective actions in the Lorentz and Axial gauges are invariant under the BRS transformations: δφ i (x) = δ BRS φ i (x)δΛ (1) where δ BRS φ i (x) is given in 1) , and the gauge and (anti)ghost fields are generically denoted by φ i .