Editing Loop quantum gravity (section)

=== Background-independent scattering amplitudes ===
{{main|Scattering amplitude}}

Loop quantum gravity is formulated in a background-independent language. No spacetime is assumed a priori, but rather it is built up by the states of theory themselves – however scattering amplitudes are derived from <math>n</math>-point functions ([[Correlation function (quantum field theory)|Correlation function]]) and these, formulated in conventional quantum field theory, are functions of points of a background spacetime. The relation between the background-independent formalism and the conventional formalism of quantum field theory on a given spacetime is not obvious, and it is not obvious how to recover low-energy quantities from the full background-independent theory. One would like to derive the <math>n</math>-point functions of the theory from the background-independent formalism, in order to compare them with the standard perturbative expansion of quantum general relativity and therefore check that loop quantum gravity yields the correct low-energy limit.

A strategy for addressing this problem has been suggested;{{sfn|Modesto|Rovelli|2005|p=191301}} by studying the boundary amplitude, namely a path integral over a finite spacetime region, seen as a function of the boundary value of the field.{{sfn|Oeckl|2003a|pp=318–324}}{{sfn|Oeckl|2003b|pp=5371–5380}} In conventional quantum field theory, this boundary amplitude is well–defined{{sfn|Conrady|Rovelli|2004|p=4037}}{{sfn|Doplicher|2004|p=064037}} and codes the physical information of the theory; it does so in quantum gravity as well, but in a fully background–independent manner.{{sfn|Conrady|Doplicher|Oeckl|Rovelli|2004|p=064019}} A generally covariant definition of <math>n</math>-point functions can then be based on the idea that the distance between physical points – arguments of the <math>n</math>-point function is determined by the state of the gravitational field on the boundary of the spacetime region considered.

Progress has been made in calculating background-independent scattering amplitudes this way with the use of spin foams. This is a way to extract physical information from the theory. Claims to have reproduced the correct behaviour for graviton scattering amplitudes and to have recovered classical gravity have been made. "We have calculated Newton's law starting from a world with no space and no time." – Carlo Rovelli.