Designations

Let us mark three-dimensional indices with Latin letters, four-dimensional indices running values 0,1,2,3 by Greek ones. All components of four-dimensional vectors are real numbers. We introduce two kinds of four-dimensional tensors. Thus, for four-dimensional coordinates by definition we have

xµ = (x0, x1, x2, x3) = (ct, x, y, z),

xµ = (x0, x1, x2, x3) = (ct,−x,−y,−z). Four-dimensional vectors with upper (low) index we name contravariant (covariant) vectors. In the same way the difference is made for covariant and contravariant tensors with the rank higher than one. Let us define the metric tensor

gµν =

  1 0 0 0 0 −1 0 0 0 0 −1 0 0 0 0 −1

  .