Symmetries and Fields in Randers-Finsler spacetime

We study the symmetries of the Lorentz violating Randers-Finsler spacetime. The privileged frame defined by the background vector diagonalises the deformed mass-shell and provides an anisotropic observer transformations. The particle Randers transformations are achieved through the Finslerian Killing equation which also shows the equivalence between observer and particle Randers transformation. For a constant background vector, the Randers transformations can be regarded as a deformed directional-dependent Poincar\'e transformation. The Randers algebra is a deformed Poincar\'e algebra whose structure coefficients are given by the Randers metric. We propose a field theory invariant over the Randers transformations. The dynamics exhibits nonlocal operators which yields to Lorentz violating terms of the nonminimal SME. The relation and implications of the Randers algebra with other Lorentz violating theories are discussed.