Quantum Gravity, Dynamical Phase Space and String Theory

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.

9 pages. Essay written for the Gravity Research Foundation 2014 Awards for Essays on Gravitation - honorable mention

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• The principle of relative locality
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Cited by in corpus (56)

• Born Reciprocity in String Theory and the Nature of Spacetime
• Quantum Gravity, Dynamical Phase Space and String Theory
• A sensitive search for wormholes
• Quantum Spaces are Modular
• A Unique Connection for Born Geometry
• On the Non-commutativity of Closed String Zero Modes
• Generalised Kinematics for Double Field Theory
• Intrinsic non-commutativity of closed string theory
• Generalized uncertainty principle or curved momentum space?
• A new wormhole solution in de Sitter space
• The Theory of Metaparticles
• T-Dual Cosmological Solutions of Double Field Theory II
• Testing ER=EPR
• $B$-decay anomalies and scalar leptoquarks in unified Pati-Salam models from noncommutative geometry
• On de Sitter Spacetime and String Theory
• Kappa-Deformations: Historical Developments and Recent Results
• The Higgs Mass, Superconnections and the TeV-scale Left-Right Symmetric Model
• The minimal length: a cut-off in disguise?
• Pati-Salam Unification from Non-commutative Geometry and the TeV-scale $W_R$ boson
• Para-Hermitian Geometries for Poisson-Lie Symmetric $\sigma$-models
• The Vacuum Energy Density and Gravitational Entropy
• Modified Dark Matter: Relating Dark Energy, Dark Matter and Baryonic Matter
• Quantum Gravity Phenomenology in the Infrared
• Geometry of multi-particle systems with a relativistic deformed kinematics and the relative locality principle
• Triple Interference, Non-linear Talbot Effect and Gravitization of the Quantum
• Gravitizing the Quantum
• Relativistic Extended Uncertainty Principle from Spacetime Curvature
• The Nonlinear Field Space Theory
• Testing Modified Dark Matter with Galaxy Clusters: Does Dark Matter know about the Cosmological Constant?
• Quantum gravity phenomenology at the dawn of the multi-messenger era -- A review
• Reinterpreting deformed Heisenberg algebras
• On the Physics of the Minimal Length: The Question of Gauge Invariance
• Quantizations of D=3 Lorentz symmetry
• Space and time transformations with a minimal length
• Nonlinear Field Space Cosmology
• Metastring Theory and Modular Space-time
• Interference and Oscillation in Nambu Quantum Mechanics
• Dimensional flow in the kappa-deformed space-time
• Minisuperspace model of compact phase space gravity
• Phase space quantization, noncommutativity and the gravitational field
• On Stringy de Sitter Spacetimes
• Modular polymer representations of the Weyl algebra
• Interactions as conformal intertwiners in 4D QFT
• On the Emergent "Quantum" Theory in Complex Adaptive Systems
• Topological Phases for Extended Objects: Semiclassical Phase-Space Approach with Tensorial Coordinates
• Towards quantum Mechanics on the curved cotangent bundle
• String Theory Bounds on the Cosmological Constant, the Higgs mass, and the Quark and Lepton Masses
• Observable Effects of Quantum Gravity
• Quantum reference frames and triality
• Extending dualities to trialities deepens the foundations of dynamics
• Spacetime defects and group momentum space
• Constraints on a Generalization of Geometric Quantum Mechanics from Neutrino and $B^0$-$\overline{B^0}$ Oscillations
• Born Lie algebras
• Born geometry via Künneth structures and recursion operators
• Three-dimensional gravity and deformations of relativistic symmetries
• The Schrödinger Equation Describes a Particular Quantum Geometry