The SubstituteTensorIndices substitutes indices in tensors. Nowhere else are the indices substituted, and the substitution can be performed in a covariant index, the corresponding contravariant one, or in both.

The tensors where indices are substituted are re-evaluated after substitution; this re-evaluation can optionally be suppressed giving the argument evaluatetensor = false. The expression where these re-evaluated tensors are introduce is by default not re-evaluated; you can change that passing the optional argument evaluateexpression = true.

To check and determine the free and repeated indices of an expression use Check.

The Physics[SubstituteTensorIndices] command was introduced in Maple 16.

For more information on Maple 16 changes, see Updates in Maple 16.

Landau, L.D., and Lifshitz, E.M. The Classical Theory of Fields, Course of Theoretical Physics Volume 2, fourth revised English edition. Elsevier, 1975.