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      Geometric description of the Schr\"odinger equation in 3n+1 dimensional configuration space

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          Abstract

          We show that for non-relativistic free particles, the (bosonic) many particle equations can be rewritten in geometric fashion in terms of a classical theory of conformally stretched spacetime. We further generalize the results for the particles subject to a potential.

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          A Collective Description of Electron Interactions. I. Magnetic Interactions

          David Bohm, David Pines (1951)
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            The Amplituhedron

            Nima Arkani-Hamed, Jaroslav Trnka (2013)
            Perturbative scattering amplitudes in gauge theories have remarkable simplicity and hidden infinite dimensional symmetries that are completely obscured in the conventional formulation of field theory using Feynman diagrams. This suggests the existence of a new understanding for scattering amplitudes where locality and unitarity do not play a central role but are derived consequences from a different starting point. In this note we provide such an understanding for N=4 SYM scattering amplitudes in the planar limit, which we identify as ``the volume" of a new mathematical object--the Amplituhedron--generalizing the positive Grassmannian. Locality and unitarity emerge hand-in-hand from positive geometry.
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              Entropic force, noncommutative gravity and ungravity

              Piero Nicolini (2010)
              After recalling the basic concepts of gravity as an emergent phenomenon, we analyze the recent derivation of Newton's law in terms of entropic force proposed by Verlinde. By reviewing some points of the procedure, we extend it to the case of a generic quantum gravity entropic correction to get compelling deviations to the Newton's law. More specifically, we study: (1) noncommutative geometry deviations and (2) ungraviton corrections. As a special result in the noncommutative case, we find that the noncommutative character of the manifold would be equivalent to the temperature of a thermodynamic system. Therefore, in analogy to the zero temperature configuration, the description of spacetime in terms of a differential manifold could be obtained only asymptotically. Finally, we extend the Verlinde's derivation to a general case, which includes all possible effects, noncommutativity, ungravity, asymptotically safe gravity, electrostatic energy, and extra dimensions, showing that the procedure is solid versus such modifications.
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                Author and article information

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                Publication date Created: 2017-03-29
                Article
                ArXiV ID: 1703.09901
                SO-VID: a92f2de8-900c-48f9-92b9-39d1163544e7
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                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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                Comments 6 pages
                Categories hep-th

                ScienceOpen disciplines: High energy & Particle physics
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                ScienceOpen disciplines: High energy & Particle physics

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