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 documentation:ref:diracorder [2015/11/20 19:56]poslavskysv [Examples] documentation:ref:diracorder [2015/11/21 12:33] Line 1: Line 1: - ====== DiracOrder ====== - ---- - - ====Description==== - - * ''​%%DiracOrder%%''​ brings all products of $\gamma$-matrices to alphabetical order - - * By default ''​%% DiracOrder%%''​ works in $D = 4$; for arbitrary $D$ one can use option ''​%% DiracOrder[[Dimension:​ D]]%%''​ - - * One can directly set trace of identity matrix (e.g. for dimensional regularisation):​ ''​%% DiracOrder[[Dimension:​ D, TraceOfOne: 4]]%%''​ - - * By default ''​DiracOrder''​ uses notation ''​G_m''​ for $\gamma_m$ and ''​G5''​ for $\gamma_5$. ''​%% DiracOrder[[Gamma:​ G, Gamma5: G5]]%%''​ specifies the notation for $\gamma_m$, $\gamma_5$ and Levi-Civita tensor. - - ====Examples==== - ---- - Order product of $\gamma$-matrices:​ - - defineMatrices '​G_a',​ '​G5',​ Matrix1.matrix - def dOrder = DiracOrder - println dOrder >> '​G_b*G_a'​.t - ​ - - > 2*g_{ba}-G_{a}*G_{b} - ​ - - println dOrder >> '​G_d*G_c*G_b*G_a'​.t - ​ - - > G_{a}*G_{b}*G_{c}*G_{d}-2*G_{c}*G_{d}*g_{ab}+2*G_{b}*G_{d}*g_{ac}-2*G_{b}*G_{c}*g_{ad} - ​-2*G_{a}*G_{d}*g_{bc}+4*g_{ad}*g_{bc}+2*G_{a}*G_{c}*g_{bd}-4*g_{ac}*g_{bd} - ​-2*G_{a}*G_{b}*g_{cd}+4*g_{ab}*g_{cd} - ​ - - ---- - All $\gamma_5$ will be shift right: - - defineMatrices '​G_a',​ '​G5',​ Matrix1.matrix - def dOrder = DiracOrder - println dOrder >> '​G5*G_b*G_a'​.t - ​ - - > 2*G5*g_{ba}-G_{a}*G_{b}*G5 - ​ - - - ---- - Use another notation for $\gamma$-matrices:​ - - defineMatrices '​F_a',​ '​F5',​ Matrix1.matrix - def dOrder = DiracOrder[[Gamma:​ '​F_a',​ Gamma5: '​F5'​]] - println dOrder >> '​F_b*F_a'​.t - ​ - - > 2*g_{ba}-F_{a}*F_{b} - ​ - - - ====See also==== - * Related guides: [[documentation:​guide:​applying_and_manipulating_transformations]],​ [[documentation:​guide:​Setting up matrix objects]], [[documentation:​guide:​list_of_transformations]] - * Related transformations:​ [[documentation:​ref:​DiracSimplify]],​ [[documentation:​ref:​DiracTrace]],​ [[documentation:​ref:​SpinorsSimplify]] - * JavaDocs: [[http://​api.redberry.cc/​redberry/​1.1.8/​java-api//​cc/​redberry/​physics/​feyncalc/​DiracOrderTransformation.html| DiracOrderTransformation]] - * Source code: [[https://​bitbucket.org/​redberry/​redberry/​src/​tip/​physics/​src/​main/​java/​cc/​redberry/​physics/​feyncalc/​DiracOrderTransformation.java|DiracOrderTransformation.java]]