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      Bipartite-Finsler spaces and the bumblebee model

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          Abstract

          We present a proposal to include Lorentz-violating effects in gravitational field by means of the Finsler geometry. In the Finsler set up, the length of an event depends both on the point and the direction in the space-time. We briefly review the bumblebee model, where the Lorentz violation is induced by a spontaneous symmetry breaking due to the bumblebee vector field.The main geometrical concepts of the Finsler geometry are outlined. Using a Finslerian Einstein-Hilbert action we derive the bumblebee action from the bipartite Finsler function with a correction to the gravitational constant.

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          CPT Violation and the Standard Model

          Don Colladay, Alan Kostelecky (1997)
          Spontaneous CPT breaking arising in string theory has been suggested as a possible observable experimental signature in neutral-meson systems. We provide a theoretical framework for the treatment of low-energy effects of spontaneous CPT violation and the attendant partial Lorentz breaking. The analysis is within the context of conventional relativistic quantum mechanics and quantum field theory in four dimensions. We use the framework to develop a CPT-violating extension to the minimal standard model that could serve as a basis for establishing quantitative CPT bounds.
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            Gravity, Lorentz Violation, and the Standard Model

            Alan Kostelecky (2003)
            The role of the gravitational sector in the Lorentz- and CPT-violating Standard-Model Extension (SME) is studied. A framework is developed for addressing this topic in the context of Riemann-Cartan spacetimes, which include as limiting cases the usual Riemann and Minkowski geometries. The methodology is first illustrated in the context of the QED extension in a Riemann-Cartan background. The full SME in this background is then considered, and the leading-order terms in the SME action involving operators of mass dimension three and four are constructed. The incorporation of arbitrary Lorentz and CPT violation into general relativity and other theories of gravity based on Riemann-Cartan geometries is discussed. The dominant terms in the effective low-energy action for the gravitational sector are provided, thereby completing the formulation of the leading-order terms in the SME with gravity. Explicit Lorentz symmetry breaking is found to be incompatible with generic Riemann-Cartan geometries, but spontaneous Lorentz breaking evades this difficulty.
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              Finsler geometric extension of Einstein gravity

              Mattias Wohlfarth, Christian Pfeifer (2011)
              We construct gravitational dynamics for Finsler spacetimes in terms of an action integral on the unit tangent bundle. These spacetimes are generalizations of Lorentzian metric manifolds which satisfy necessary causality properties. A coupling procedure for matter fields to Finsler gravity completes our new theory that consistently becomes equivalent to Einstein gravity in the limit of metric geometry. We provide a precise geometric definition of observers and their measurements, and show that the transformations by means of which different observers communicate form a groupoid that generalizes the usual Lorentz group. Moreover, we discuss the implementation of Finsler spacetime symmetries. We use our results to analyze a particular spacetime model that leads to Finsler geometric refinements of the linearized Schwarzschild solution.
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                Author and article information

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                Publication date Created: 18 September 2013
                Article
                DOI: 10.1142/9789814566438_0066
                ArXiV ID: 1309.4671
                SO-VID: 0ab6a175-3d67-458d-a991-705330e60b50
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                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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                Comments Presented at the Sixth Meeting on CPT and Lorentz Symmetry, Bloomington, Indiana, June 17-21, 2013
                Categories hep-th

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