## Four-Vector

A four-element vector

 (1)

which transforms under a Lorentz Transformation like the Position Four-Vector. This means it obeys
 (2)

 (3)

 (4)

where is the Lorentz Tensor. Multiplication of two four-vectors with the Metric gives products of the form
 (5)

In the case of the Position Four-Vector, (where is the speed of light ) and this product is an invariant known as the spacetime interval.

Morse, P. M. and Feshbach, H. The Lorentz Transformation, Four-Vectors, Spinors.'' §1.7 in Methods of Theoretical Physics, Part I. New York: McGraw-Hill, pp. 93-107, 1953.