Recognize the basic use or purpose of Christoffel symbols in the study of quantum gravity theory. These symbols describe the gravitational force field in terms of a metric tensor. Metric tensors are mathematical, or more specifically geometric, functions that define vectors that are tangents to a curved space. They can be used to describe the distance between or the length of one of these vectors. The end result is a real number that can be used as a general description of the vectors.
Quantize the gravitational field functions corresponding to the gravitational field, using quantum inverse scattering. Quantum inverse scattering is the method of quantifying classical integrable differential equations by solving a pair of matrices that are dependent upon time as one of the variables. This time dimension is then applied to a second step that involves solving quantum models based on one space and one time coordinate.
Plug in the quantized vectors to determine the metric tensor. The metric tensor is important for understanding and quantifying the gravitational force field because in classical physics, the metric tensor indicates the gravitational potential for the field. By basically working backward from the known facts regarding the vectors describing the space-time connection, you arrive at a quantifiable amount for the tensor/gravitational force field. The Christoffel symbols can then be used in terms of either the time or motion component of gravitational force. Working in reverse from the metric tensor, you can then arrive at the values represented by the Christoffel symbols.