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documentation:ref:diracorder [2015/11/20 20:05]
poslavskysv [Description]
documentation:ref:diracorder [2015/11/21 12:33]
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-====== 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 $\gamma_m$ and $\gamma_5$. 
- 
-====Examples==== 
----- 
-Order product of $\gamma$-matrices:​ 
-<sxh groovy; gutter: true> 
-defineMatrices '​G_a',​ '​G5',​ Matrix1.matrix 
-def dOrder = DiracOrder 
-println dOrder >> '​G_b*G_a'​.t 
-</​sxh>​ 
-<sxh plain; gutter: false> 
-   > 2*g_{ba}-G_{a}*G_{b} 
-</​sxh>​ 
-<sxh groovy; gutter: true; first-line: 4> 
-println dOrder >> '​G_d*G_c*G_b*G_a'​.t 
-</​sxh>​ 
-<sxh plain; gutter: false> 
-   > 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} 
-</​sxh>​ 
- 
----- 
-All $\gamma_5$ will be shift right: 
-<sxh groovy; gutter: true> 
-defineMatrices '​G_a',​ '​G5',​ Matrix1.matrix 
-def dOrder = DiracOrder 
-println dOrder >> '​G5*G_b*G_a'​.t 
-</​sxh>​ 
-<sxh plain; gutter: false> 
-   > 2*G5*g_{ba}-G_{a}*G_{b}*G5 
-</​sxh>​ 
- 
- 
----- 
-Use another notation for $\gamma$-matrices:​ 
-<sxh groovy; gutter: true> 
-defineMatrices '​F_a',​ '​F5',​ Matrix1.matrix 
-def dOrder = DiracOrder[[Gamma:​ '​F_a',​ Gamma5: '​F5'​]] 
-println dOrder >> '​F_b*F_a'​.t 
-</​sxh>​ 
-<sxh plain; gutter: false> 
-   > 2*g_{ba}-F_{a}*F_{b} 
-</​sxh>​ 
- 
- 
-====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]]