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 documentation:ref:diracsimplify [2015/11/21 10:15]poslavskysv [See also] documentation:ref:diracsimplify [2015/11/21 12:33] Line 1: Line 1: - ====== DiracSimplify ====== - ---- - ====Description==== - - * ''​%%DiracSimplify%%''​ simplifies products of gamma matrices - - * By default ''​%%DiracSimplify%%''​ works in $D = 4$; for arbitrary $D$ one can use option ''​%%DiracSimplify[[Dimension:​ D]]%%''​ - - * One can directly set trace of identity matrix (e.g. for dimensional regularisation):​ ''​%%DiracSimplify[[Dimension:​ D, TraceOfOne: 4]]%%''​ - - * By default ''​DiracSimplify''​ uses notation ''​G_m''​ for $\gamma_m$ and ''​G5''​ for $\gamma_5$. ​ ''​%%DiracSimplify[G,​ G5]%%''​ or ''​%% DiracSimplify[[Gamma:​ G, Gamma5: G5]]%%''​ specifies the notation for $\gamma_m$ and $\gamma_5$. - - * ''​%% DiracSimplify[[Simplifications:​ rules]]%%''​ will apply additional simplification ''​rules''​ to each processed product of gammas - - - ====Examples==== - ---- - Simplify different expressions:​ - - defineMatrices '​G_a',​ '​G5',​ Matrix1.matrix - def dSimplify = DiracSimplify - println dSimplify >> '​G_a*G^a'​.t - ​ - - > 4 - ​ - - println dSimplify >> '​G_a*G_b*G^a'​.t - ​ - - > -2*G_{b} - ​ - - println dSimplify >> '​G_a*G_b*G^a*G^b'​.t - ​ - - > -8 - ​ - - println dSimplify >> '​G5*G_a*G_b*G^a*G^b*G5*G5'​.t - ​ - - > -8*G5 - ​ - - println dSimplify >> '​G5*G_a*G_b*G^a*G5*G5'​.t - ​ - - > 2*G_{b} - ​ - - ---- - Simplify in different dimensions: - - defineMatrices '​G_a',​ '​G5',​ Matrix1.matrix - def dSimplify = DiracSimplify[[Dimension:​ '​D'​]] - println dSimplify >> '​G_a*G^a'​.t - ​ - - > D - ​ - - println dSimplify >> '​G_a*G_b*G^a'​.t - ​ - - > -(-2+D)*G_{b} - ​ - - ---- - Specify additional simplifications:​ - - defineMatrices '​G_a',​ '​G5',​ Matrix1.matrix - def dSimplify = DiracSimplify[[Simplifications:​ '​p_a*k^a = s'.t]] - println dSimplify >> '​p^b*k^c*G_a*G_b*G_c*G^a'​.t - ​ - - > 4*s - ​ - ====See also==== - * Related guides: [[documentation:​guide:​applying_and_manipulating_transformations]],​ [[documentation:​guide:​Setting up matrix objects]], [[documentation:​guide:​list_of_transformations]] - * Related tutorials: [[documentation:​tutorials:​Compton scattering in QED]] - * Related transformations:​ [[documentation:​ref:​DiracTrace]],​ [[documentation:​ref:​spinorssimplify]],​ [[documentation:​ref:​DiracOrder]], ​ [[documentation:​ref:​LeviCivitaSimplify]],​ [[documentation:​ref:​UnitarySimplify]],​ [[documentation:​ref:​UnitaryTrace]] - * JavaDocs: [[http://​api.redberry.cc/​redberry/​1.1.8/​java-api//​cc/​redberry/​physics/​feyncalc/​DiracSimplifyTransformation.html| DiracSimplifyTransformation]] - * Source code: [[https://​bitbucket.org/​redberry/​redberry/​src/​tip/​physics/​src/​main/​java/​cc/​redberry/​physics/​feyncalc/​DiracSimplifyTransformation.java|DiracSimplifyTransformation.java]]