Quantum Gravity models - brief conceptual summary

Abstract

After short historical overview we describe the difficulties with application of standard QFT methods in quantum gravity (QG). The incompatibility of QG with the use of classical continuous space-time required conceptually new approach. We present briefly three proposals: loop quantum gravity (LQG), the field-theoretic framework on noncommutative space-time and QG models formulated on discretized (triangularized) space-time. We evaluate these models as realizing expected important properties of QG: background independence, consistent quantum diffeomorphisms, noncommutative or discrete structure of space-time at very short distances, finite/renormalizable QG corrections. We only briefly outline an important issue of embedding QG into larger geometric and dynamical frameworks (e.g. supergravity, (super)strings, p-branes, M-theory), with the aim to achieve full unification of all fundamental interactions.

arXiv comment24 pages; invited article for the book "Mathematical Structure of the Universe", publ. Copernicus Center Press, Copernicus Center for Interdisciplinary Studies, Cracow 2014, p.277-300; v2:the text (besides added Abstract and Contents in hep version) as published in the book, with minor errors corrected, references ordered alphabetically

References in corpus (33)

• Large N Field Theories, String Theory and Gravity
• f(R) Theories Of Gravity
• The World as a Hologram
• Quantum Gravity at a Lifshitz Point
• The quantum structure of spacetime at the Planck scale and quantum fields
• Nonperturbative Evolution Equation for Quantum Gravity
• Extended Theories of Gravity and their Cosmological and Astrophysical Applications
• Testable scenario for Relativity with minimum-length
• Bicrossproduct structure of $\kappa$-Poincare group and non-commutative geometry
• Emergence of a 4D World from Causal Quantum Gravity
• Classical and Quantum Mechanics of Free \k Relativistic Systems
• On Background Independent Open-String Field Theory
• Asymptotic perfect fluid dynamics as a consequence of AdS/CFT
• 3d Quantum Gravity and Effective Non-Commutative Quantum Field Theory
• Doubly Special Relativity theories as different bases of $\kappa$--Poincaré algebra
• Twistor actions for non-self-dual fields; a new foundation for twistor-string theory
• Doubly Special Relativity versus $\kappa$-deformation of relativistic kinematics
• Second Order Noncommutative Corrections to Gravity
• Lie algebraic Noncommutative Gravity
• Quantum Gravity via Causal Dynamical Triangulations
• Emergent Relativity
• Operator Spin Foam Models
• Conformal and Einstein gravity from twistor actions
• Covariant Realization of Quantum Spaces as Star Products by Drinfeld Twists
• $\kappa$-Minkowski Spacetimes and DSR Algebras: Fresh Look and Old Problems
• De Sitter Universe from Causal Dynamical Triangulations without Preferred Foliation
• Multiparticle extension of the higher-spin algebra
• Gamma ray burst delay times probe the geometry of momentum space
• Dynamical symmetries in noncommutative theories
• Quantum Field Theory on Quantum Spacetime
• Algebraic approach to quantum gravity II: noncommutative spacetime
• Twisting all the way: from algebras to morphisms and connections
• Twists of quantum groups and noncommutative field theory

Cited by in corpus (1)

• Uncertainty relation for quantum gravity