A Lorentz invariant is a scalar quantity unchanged by every Lorentz transformation. If 
belongs to the Lorentz group,
a function 
on Minkowski space is Lorentz
invariant when
 |
for every vector 
. The basic example is the quadratic
form defined by the Minkowski metric; in
one common sign convention,
 |
More generally, complete tensor contractions of Lorentz tensors are Lorentz invariant. A quantity whose components change under a Lorentz transformation may therefore still determine a Lorentz invariant after its indices are contracted.
