  A new definition for the path integral is proposed in terms of Finsler
geometry. The conventional Feynman's scheme for quantisation by Lagrangian
formalism suffers problems due to the lack of geometrical structure of the
configuration space where the path integral is defined. We propose that, by
implementing the Feynman's path integral on an extended configuration space
endowed with a Finsler structure, the formalism could be justified as a proper
scheme for quantisation from Lagrangian only, that is, independent from
Hamiltonian formalism. The scheme is coordinate free, and also a covariant
framework which does not depend on the choice of time coordinate.
