Relativistic invariant

A relativistic invariant or Lorentz scalar is a Scalar quantity that is invariant under a Lorentz transformation.

The most common invariant is the Scalar product of two four-vectors:

a\cdot b=-a_{0}b_{0}+a_{1}b_{1}+a_{2}b_{2}+a_{3}b_{3}=a_{\mu}b_{\nu}g^{\mu\nu}

$g^{\mu\nu}$ is the metric tensor. By extension, the norm of a four-vector is also invariant:

|a|^{2}=g_{\mu\nu}a^{\mu}a^{\nu}

Other important invariants include the proper time, electric charge and rest mass.