N ov 2 00 5 Quantized gauge - affine gravity in the superfiber bundle approach

The quantization of gauge-affine gravity within the superfiber bundle formalism is proposed. By introducing an even pseudotensorial 1-superform over a principal superfiber bundle with superconnection, we obtain the geometrical Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST transformations of the fields occurring in such a theory. Reducing the four-dimensional general affine group double-covering GA(4, R) to the Poincaré group double-covering ISO(1, 3) we also find the BRST and anti-BRST transformations of the fields present in Einstein's gravity. Furthermore, we give a prescription leading to the construction of both BRST-invariant gauge-fixing action for gauge-affine gravity and Einstein's gravity.