In the two previous chapters we have discussed applications of loop gravity to physically relevant, but specific situations – black holes and early cosmology. How to extract the entire information from the theory systematically, and compare it with the usual way of doing high-energy physics?

In conventional field theory, knowledge of the n-point functions

W(x1,…,xn) = 〈0|ø(xn)…ø(x1)|0〉,

amounts to the complete knowledge of the theory, as emphasized by Arthur Wightman in the 1950s (Wightman 1959). From these functions we can compute the scattering amplitudes and everything else. Can we recover the value of all these functions, from the theory we have defined in this book? This, for instance, would allow us to compare the theory with the effective perturbative quantum theory of general relativity, which, although non-renormalizable is nevertheless usable at low energy. More generally, it would connect the abstruse background-independent formalism needed for defining quantum gravity in general with the tools of quantum field theory that we are used to, from flat space physics.

The answer is yes, the value of the n-point functions can be computed from the theory we have defined in this book. This requires a careful understanding of how the information about the background around which the n-point functions are defined is dealt with in the background-independent theory. This is done in this chapter.