Spacetime formalism. In my view, thedevelopment of continuous spacetime formalisms, [181, 160,26, 143], is one of the most promising areas of development of thetheory, because it might be the key for addressing most of the open problems. First,a spacetime formalism frees us from the obscurities of the frozen time formalism,and allows an intuitive, Feynman-style, description of the dynamics of quantumspacetime. I think that the classical limit, the quantum description of black holes,or graviton-graviton scattering, just to mention a few examples, could be addressedmuch more easily in the covariant picture. Second, it allows the general ideas ofHartle [102] and Isham [118, 119, 122,121] on the interpretation ofgenerally covariant quantum theories to be applied in loop quantum gravity. Thiscould drastically simplify the complications of the canonical way of dealing withgeneral covariant observables [169,167]. Third, the spacetime formalismshould suggest solutions to the problem of selecting the correct hamiltonianconstraint: it is usually easier to deal with invariances in the Lagrangian ratherthan in the hamiltonian formalisms. The spacetime formalism is just born, and muchhas to be done. See the original papers for suggestions and open problems.
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