Quantization of the gravitational field: the presentation of gravity as the Hilbert space of the quantized system

In the last three decades or so many methods to quantize the gravitational field were developed but all of them have led to no, or very little progress. All these methods are shared in the idea of treating gravitation in a similar fashion to either the electromagnetic field or the Yang-Mills field. The author suggests a completely new approach to the notion of quantizing gravity. In this approach the gravitational field is to be described as the Hilbert or the Banach space of the quantized system, whereas all other non-gravitational physical quantities are to be described as operators in the infinite-dimensional space. This idea is in complete harmony with Einstein's notion that gravitation is to be treated differently from other fields and hence led him to identify gravity with the Riemannian geometry of space-time, whereas other non-gravitational fields are left to be described as quantities defined in that Riemannian geometry. (Auth.)