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# 3-Vector, 4-Vector, and Scalar Product

The three space components of a contravariant 4-vector, , form a 3-vector.

 (2.12)

where .

The scalar product of a 3-vector is defined as

 (2.13)

Sometimes we omit the index and denote a 4-vector, , by just . We can thus write the scalar product of a 4-vector as

 (2.14)

This is often taken as the definition of the metric tensor, . We notice that can be positive, negative, or zero.

Douglas M. Gingrich (gingrich@ ualberta.ca)
2004-03-18