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Anti-Newtonian Expansions and the Functional Renormalization Group

Department of Physics and Astronomy, University of Pittsburgh, 100 Allen Hall, Pittsburgh, PA 15260, USA
Universe 2019, 5(3), 85;
Received: 14 February 2019 / Revised: 1 March 2019 / Accepted: 5 March 2019 / Published: 21 March 2019
Anti-Newtonian expansions are introduced for scalar quantum field theories and classical gravity. They expand around a limiting theory that evolves only in time while the spatial points are dynamically decoupled. Higher orders of the expansion re-introduce spatial interactions and produce overlapping lightcones from the limiting isolated world line evolution. In scalar quantum field theories, the limiting system consists of copies of a self-interacting quantum mechanical system. In a spatially discretized setting, a nonlinear “graph transform” arises that produces an in principle exact solution of the Functional Renormalization Group for the Legendre effective action. The quantum mechanical input data can be prepared from its 1 + 0 dimensional counterpart. In Einstein gravity, the anti-Newtonian limit has no dynamical spatial gradients, yet remains fully diffeomorphism invariant and propagates the original number of degrees of freedom. A canonical transformation (trivialization map) is constructed, in powers of a fractional inverse of Newton’s constant, that maps the ADM action into its anti-Newtonian limit. We outline the prospects of an associated trivializing flow in the quantum theory. View Full-Text
Keywords: anti-Newtonian limit; functional renormalization group; trivializing map anti-Newtonian limit; functional renormalization group; trivializing map
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Niedermaier, M. Anti-Newtonian Expansions and the Functional Renormalization Group. Universe 2019, 5, 85.

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