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# Covariant and Contravariant Indices

We will need to distinguish between a covariant vector and a contravariant vector. In terms of indices, we define

 covariant indices (subscript), contravariant indices (superscript).

The metric tensor is used to convert from one type of vector to the other:

 (2.10)

Normally the sum over identical indices is implied (Einstein summation convention) and we simply write . We can also rise indices: , where for a Lorentz metric. Also , where is the Kronecker symbol:

 (2.11)

Also, notice that .

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