In mathematics, mathematical physics, and theoretical physics, the spin tensor is a quantity used to describe the rotational motion of particles in spacetime. The spin tensor has application in general relativity and special relativity, as well as quantum mechanics, relativistic quantum mechanics, and quantum field theory.
The special Euclidean group SE(d) of direct isometries is generated by translations and rotations. Its Lie algebra is written .
This article uses Cartesian coordinates and tensor index notation.