====== Kronecker delta ======
----
====Basics====
The notation for Kronecked delta used in Redberry is ordinary ''d^a_b'' and similarly for other index types (''d^A_B'', ''d^\\alpha_\\beta'' etc.).  Kronecker delta are automatically symmetric:
<sxh groovy; gutter: false>
println 'd^a_b - d_b^a'.t
</sxh>
<sxh plain; gutter: false>
   > 0
</sxh>
<sxh groovy; gutter: false>
println 'd_A^B + d^B_A'.t
</sxh>
<sxh plain; gutter: false>
   > 2*d^B_A
</sxh>

Raising and lowering of Kronecker delta indices may produce [[documentation:ref:metric_tensor]]:
<sxh groovy; gutter: false>
println ('{^a -> _a}'.mapping >> 'd^a_b'.t)
</sxh>
<sxh plain; gutter: false>
   > g_ab
</sxh>

The transformation that simplifies contractions with Kronecker deltas is [[documentation:ref:eliminatemetrics]]:
<sxh groovy; gutter: false>
println EliminateMetrics >> 'd_a^m*F^ab*d_b^n'.t
</sxh>
<sxh plain; gutter: false>
   > F^mn
</sxh>

====Details====
In addition to ''d^a_b'' notation Redberry also uses ''g^a_b'', which is the notation for [[metric_tensor]] with one upper and one lower index. 

One can specify different name for Kronecker tensor by putting the following line in the beginning of the code:
<sxh groovy; gutter: false>
//change default metric name
CC.current().setKroneckerName('f')
println EliminateMetrics >> 'f_a^m*F^ab*f_b^n'.t
</sxh>
<sxh plain; gutter: false>
   > F^mn
</sxh>
=====See also=====
  * Related guides: [[documentation:guide:types_of_indices_and_metric]]
  * Reference material: [[documentation:ref:metric_tensor]], [[documentation:ref:eliminatemetrics]]