Finsler geometries can be associated with the motion of point particles in effective field theories incorporating hypothetical violations of the foundational Lorentz symmetry of relativity. Methods to construct these Finsler spaces are presented, and some of their properties are explored. This talk is summarizing the results in my recent paper, entitled “Riemann-Finsler Geometry and Lorentz-Violating Scalar Fields” written with Alan Kostelecky,
https://doi.org/10.1016/j.physletb.2018.10.011.