Wheeler-De Witt equation and the Canonical Construction of the Glauber-Sudarshan States in Quantum Gravity

Abstract

Quantum gravity is fundamentally different from the non-gravitational quantum field theories in the sense that most of the techniques derived for the latter cannot be easily extended to the former. For example, correlation functions in quantum gravity become hard to define properly if the bulk Hamiltonian -- in the absence of a boundary Hamiltonian, and as a consequence of the Wheeler-De Witt equation -- itself annihilates the states thus rendering the evolution operators to identities. An even harder problem is the back reactions of the fluctuations on the background itself. We argue that the construction of the Glauber-Sudarshan states takes care of these two issues in rather interesting ways. For the former, the displacement operators are defined at every instant of time, without directly invoking the Hamiltonian, so that they naturally extend to the path-integral description as sum over histories. For the latter, the back reactions of the fluctuations are carefully accounted for by the Schwinger-Dyson equations. In fact these back reactions are in part responsible to convert the ambient supersymmetric Minkowski background to a transient de Sitter phase. Expectedly this transient de Sitter phase is defined well within the validity regime of the trans-Planckian bound.