Abstract
Effective field theories with explicit Lorentz violation are intimately linked to Riemann–Finsler geometry. The quadratic single-fermion restriction of the Standard-Model Extension provides a rich source of pseudo-Riemann–Finsler spacetimes and Riemann–Finsler spaces. An example is presented that is constructed from a 1-form coefficient and has Finsler structure complementary to the Randers structure.
Highlights
The study of Riemann–Finsler geometry, which has roots in Riemann’s 1854 Habilitationsvortrag and Finsler’s 1918 dissertation [1,2], is an established mathematical field with a variety of physical applications
A well-known example intimately linked to physics is Randers geometry [3], in which the Riemann metric at each point is augmented by a contribution from a 1-form
The present work concerns the relationship between a large class of Riemann–Finsler geometries and theories with explicit Lorentz violation
Summary
Article history: Received 26 April 2011 Accepted 18 May 2011 Available online 23 May 2011 Editor: A. Effective field theories with explicit Lorentz violation are intimately linked to Riemann–Finsler geometry. The quadratic single-fermion restriction of the Standard-Model Extension provides a rich source of pseudo-Riemann–Finsler spacetimes and Riemann–Finsler spaces. An example is presented that is constructed from a 1-form coefficient and has Finsler structure complementary to the Randers structure
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