Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2010-04-06
Physics
High Energy Physics
High Energy Physics - Theory
Review submitted to SIGMA for Special Issue on Noncommutative Spaces and Fields, 82 pages
Scientific paper
We review a novel and authentic way to quantize gravity. This noble clue is based on the fact that Einstein gravity can be formulated in terms of symplectic geometry rather than 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 the symplectic geometry known as the Darboux theorem or the Moser lemma, one can understand how diffeomorphism symmetry arises from noncommutative U(1) gauge theory and so gravity can emerge from the noncommutative electromagnetism, which is also an interacting theory. As a consequence, it is feasible to formulate a background independent quatum gravity where the prior existence of any spacetime structure is not a priori assumed but defined by fundamental ingredients in quantum gravity theory. This scheme for quantum gravity resolves many notorious problems in theoretical physics, for example, to resolve 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 for 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 $\star$-algebra) of quantum gravity.
Lee Jungjai
Yang Hyun Seok
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