Correlações nos estados semiclássicos da gravitação quântica de laços

Abstract

The objective of this work is to investigate the correlations in the semiclassical states of Loop Quantum Gravity (LQG) and propose a new class of states compatible with semiclassical gravity. To this end, the necessary elements of General Relativity in the Cartan Formalism are first presented, followed by the presentation of the LQG formalism. Subsequently, we present established families of coherent states from the literature and show that they exhibit short-range correlations concerning area fluctuations. We then introduce a new class of perturbed coherent states, constructed from the non-local excitation of intrinsic coherent states. Finally, we demonstrate that this new class of states generates area correlations decaying as 1/d² in the semiclassical limit, which is in agreement with the expected behavior for the free massless graviton.