Quantum Gravity, Dynamical Phase Space and String Theory

TL;DR

This paper proposes a novel formulation of string theory that incorporates dynamical phase space with both space-time and momentum space being fundamental, unifying key geometric frameworks in a quantum gravity context.

Contribution

It introduces a new string theory framework with dynamical phase space, where space-time emerges as a derived concept, integrating symplectic, complex, and real geometries.

Findings

Dynamical phase space involves both space-time and momentum space.

A new Renormalization Group governs the dynamics of this phase space.

Space-time is a derived concept within this formulation.

Abstract

In a natural extension of the relativity principle we argue that a quantum theory of gravity involves two fundamental scales associated with both dynamical space-time as well as dynamical momentum space. This view of quantum gravity is explicitly realized in a new formulation of string theory which involves dynamical phase space and in which space-time is a derived concept. This formulation naturally unifies symplectic geometry of Hamiltonian dynamics, complex geometry of quantum theory and real geometry of general relativity. The space-time and momentum space dynamics, and thus dynamical phase space, is governed by a new version of the Renormalization Group.