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Section 1 of Schweber [ ], or Section 7.

In the second, the very active period after until the s to s will be reviewed. Metrical structure The first is a prescription for the definition of the distance ds between two infinitesimally close points on MD, eventually corresponding to temporal and spatial distances in the external world.

In Finsler geometry, the line element depends not only on the coordinates xi of a point on the manifold, but also on the infinitesimal elements of direction between neighbouring points dxi: 12 Again, gij is required to be homogeneous of rank 1. Relativistic Quantum Field Theory is a mathematical scheme to describe the sub-atomic particles and forces. Nevertheless, we will almost exclusively be dealing with the extension of geometry and of the number of space dimensions.

We briefly describe the mathematical objects occurring in an order that goes from the less structured to the more structured cases.