Clock and Category; IS QUANTUM GRAVITY ALGEBRAIC

Abstract

We investigate the possibility that the quantum theory of gravity could be constructed discretely using algebraic methods. The algebraic tools are similar to ones used in constructing topological quantum field theories.The algebraic tools are related to ideas about the reinterpretation of quantum mechanics in a general relativistic context.

To appear in special issue of JMP. Latex document

References in corpus (2)

• Four dimensional topological quantum field theory, Hopf categories, and the canonical bases
• Structure of Topological Lattice Field Theories in Three Dimensions

Cited by in corpus (43)

• Relational Quantum Mechanics
• Loop Quantum Gravity
• Relativistic spin networks and quantum gravity
• Spin Foam Models
• ``Sum over Surfaces'' form of Loop Quantum Gravity
• Linking Topological Quantum Field Theory and Nonperturbative Quantum Gravity
• Spacetime geometry from algebra: spin foam models for non-perturbative quantum gravity
• Topos Theory and Consistent Histories: The Internal Logic of the Set of all Consistent Sets
• Quantum deformation of quantum gravity
• Switching internal times and a new perspective on the 'wave function of the universe'
• SL(2,C) Chern-Simons Theory, a non-Planar Graph Operator, and 4D Loop Quantum Gravity with a Cosmological Constant: Semiclassical Geometry
• Cauchy Slice Holography: A New AdS/CFT Dictionary
• The geometry of quantum spin networks
• Cell 2-representations of finitary 2-categories
• A holographic formulation of quantum general relativity
• Implementing causality in the spin foam quantum geometry
• Toolbox for reconstructing quantum theory from rules on information acquisition
• The strong and weak holographic principles
• Nambu Quantum Mechanics: A Nonlinear Generalization of Geometric Quantum Mechanics
• Schwarzschild horizon dynamics and SU(2) Chern-Simons theory
• An algebraic interpretation of the Wheeler-DeWitt equation
• Noncommutativity and Discrete Physics
• On de Sitter Spacetime and String Theory
• The Cosmological Constant and the Deconstruction of Gravity
• Quantum deformation of quantum cosmology: A framework to discuss the cosmological constant problem
• Finite Number of States, de Sitter Space and Quantum Groups at Roots of Unity
• Quantum geometry from higher gauge theory
• Diagrams and discrete extensions for finitary 2-representations
• Triple Interference, Non-linear Talbot Effect and Gravitization of the Quantum
• A candidate for a background independent formulation of M theory
• A note on entanglement entropy and quantum geometry
• Invariants of 4-manifolds from Khovanov-Rozansky link homology
• (Super)gravity and Yang-Mills Theories as Generalized Topological Fields with Constraints
• The thermodynamics of quantum spacetime histories
• Graded dimensions and monomial bases for the cyclotomic quiver Hecke algebras
• `Iconoclastic', Categorical Quantum Gravity
• Finitary Topos for Locally Finite, Causal and Quantal Vacuum Einstein Gravity
• Regular obstructed categories and TQFT
• Diffeomorphisms from finite triangulations and absence of 'local' degrees of freedom
• Reflections on Topological Quantum Field Theory
• Non-commutative fermion mass matrix and gravity
• An action of the Hecke monoid on rational modules for the Borel subgroup of a quantised general linear group
• The Physics Inside Topological Quantum Field Theories