SL(2,C) Gauge Theory of Gravitation and the Quantization of the Gravitational Field

A new approach to quantize the gavitationalfield is presented. It is based on the observation thatthe quantum character of matter becomes more significantas one gets closer to the big bang. As the metric loses its meaning, it makes sense to considerSchrodinger's three generic types of manifolds —unconnected differentiable, affinely connected, andmetrically connected — as a temporal sequencefollowing the big bang. Hence one should quantize thegravitational field on general differentiable manifoldsor on affinely connected manifolds. The SL(2,C) gaugetheory of gravitation is employed to explore thispossibility. Within this framework, the quantization itselfmay well be canonical.