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 — documentation:ref:kronecker_delta [2015/11/21 12:33] (current) Line 1: Line 1: + ====== 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: + + println 'd^a_b - d_b^a'​.t + ​ + + > 0 + ​ + + println 'd_A^B + d^B_A'​.t + ​ + + > 2*d^B_A + ​ + + Raising and lowering of Kronecker delta indices may produce [[documentation:​ref:​metric_tensor]]:​ + + println ('{^a -> _a}'​.mapping >> '​d^a_b'​.t) + ​ + + > g_ab + ​ + + The transformation that simplifies contractions with Kronecker deltas is [[documentation:​ref:​eliminatemetrics]]:​ + + println EliminateMetrics >> '​d_a^m*F^ab*d_b^n'​.t + ​ + + > F^mn + ​ + + ====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: + + //change default metric name + CC.current().setKroneckerName('​f'​) + println EliminateMetrics >> '​f_a^m*F^ab*f_b^n'​.t + ​ + + > F^mn + ​ + =====See also===== + * Related guides: [[documentation:​guide:​types_of_indices_and_metric]] + * Reference material: [[documentation:​ref:​metric_tensor]],​ [[documentation:​ref:​eliminatemetrics]]