Glauber-Sudarshan States, Wave Functional of the Universe and the Wheeler-De Witt equation

TL;DR

This paper explores the relationship between Glauber-Sudarshan states, the wave functional of the universe, and the Wheeler-De Witt equation, revealing that both on-shell and off-shell states are governed by a universal wave functional satisfying the Wheeler-De Witt equation, with implications for de Sitter phases in string theory.

Contribution

It demonstrates that Glauber-Sudarshan states are controlled by a universal wave functional satisfying the Wheeler-De Witt equation, linking off-shell states to the universe's wave functional.

Findings

Glauber-Sudarshan states are governed by a wave functional satisfying the Wheeler-De Witt equation.

Both on-shell and off-shell states are controlled by this wave functional.

De Sitter phases in string theory are better viewed as excited states over a Minkowski background.

Abstract

One of the pertinent question in the analysis of de Sitter as an excited state is what happens to the Glauber-Sudarshan states that are off-shell, i.e. the states that do not satisfy the Schwinger-Dyson equations. We argue that these Glauber-Sudarshan states, including the on-shell ones, are controlled by a bigger envelope wave functional namely a wave functional of the universe which surprisingly satisfies a Wheeler-De Witt equation. We provide various justification of the aforementioned identification including the determination of the emergent Hamiltonian constraint appearing in the Wheeler-De Witt equation that is satisfied by both the on- and off-shell states. Our analysis provides further evidence of why a transient four-dimensional de Sitter phase in string theory should be viewed as an excited state over a supersymmetric warped Minkowski background and not as a vacuum state.