2010/04/30 by Jungjai Lee, Hyun Seok Yang · 17 citations
Physics and Astronomy · #Advanced Mathematical Theories and Applications #Black Holes and Theoretical Physics #Entropic gravity #Euclidean quantum gravity #Hořava–Lifshitz gravity #Noncommutative and Quantum Gravity Theories #Noncommutative geometry #Noncommutative quantum field theory #Quantum geometry #Quantum gravity #Quantum spacetime #Semiclassical gravity #Spin foam #gr-qc #hep-ph #hep-th
paper · pdf · doi:10.3938/jkps.65.1754
published in Journal of the Korean Physical Society 65(11), 1754-1798 (Springer Science+Business Media) · 97 pages, to be published in J. Korean Phys. Soc
arxiv created 2014/11/25 · openalex publication_date 2014/12/01 · arxiv updated 2014/12/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We review a novel and authentic way to quantize gravity. This novel approach is based on the fact that Einstein gravity can be formulated in terms of a symplectic geometry rather than a Riemannian geometry in the context of emergent gravity. An essential step for emergent gravity is to realize the equivalence principle, the most important property in the theory of gravity (general relativity), from U (1) gauge theory on a symplectic or Poisson manifold. Through the realization of the equivalence principle, which is an intrinsic property in symplectic geometry known as the Darboux theorem or the Moser lemma, one can understand how diffeomorphism symmetry arises from noncommutative U (1) gauge theory; thus, gravity can emerge from the noncommutative electromagnetism, which is also an interacting theory. As a consequence, a background-independent quantum gravity in which the prior existence of any spacetime structure is not a priori assumed but is defined by using the fundamental ingredients in quantum gravity theory can be formulated. This scheme for quantum gravity can be used to resolve many notorious problems in theoretical physics, such as the cosmological constant problem, to understand the nature of dark energy, and to explain why gravity is so weak compared to other forces. In particular, it leads to a remarkable picture of what matter is. A matter field, such as leptons and quarks, simply arises as a stable localized geometry, which is a topological object in the defining algebra (noncommutative ★-algebra) of quantum gravity.