International Research Fellowship Program: Moving Forward in Loop Quantum Gravity Via Self-Duality

点击翻译按钮获取中文摘要

0601844EngleThe International Research Fellowship Program enables U.S. scientists and engineers to conduct nine to twenty-four months of research abroad. The program's awards provide opportunities for joint research, and the use of unique or complementary facilities, expertise and experimental conditions abroad.This award will support a twenty-four-month research fellowship by Dr. Jonathan S. Engle to work with Dr. Carlo Rovelli at Centre de Physique Theorique, in Marseille, France.Significant progress has been made over the past decade in loop quantum gravity. However, issues remain. One prominent among them is that the implementation of dynamics is conceptually somewhat unnatural and technically quite complex. A direct consequence of this is an inability to fully relate loop quantum gravity to spin-foams, the path integral version of loop quantum gravity. One way of resolving this problem is to use a self-dual formulation of general relativity. Classically, in the self-dual formulation, the dynamics are as simple as they possibly could be. However, in the past, there was an obstacle preventing the rigorous definition of a quantum theory based on the self-dual formulation: One did not know how to construct an acceptable inner-product a notion of "overlap" between states, which is essential in order to extract predictions from the theory. The goal of the project is to find an inner-product for self-dual loop quantum gravity. A number of inner products are available, including gauge and diffeomorphism-invariant ones already mentioned in the literature, as well as a class introduced by the PI. The key question is whether or not any of these implement the correct reality conditions of the self-dual theory --- that is, whether or not any of these are such that complex conjugation at the classical level carries over to Hermitian conjugation at the quantum level. If the PI is successful in finding an acceptable inner product, the PI will try to reproduce quantum geometry in the newly created self-dual framework and then attempt to construct a simplified Hamiltonian constraint. The PI will then see whether the simplified Hamiltonian constraint allows loop quantum gravity to be more directly related to a spin-foam model.