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documentation:ref:diractrace [2015/11/20 19:26] poslavskysv [Options] |
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| ====Options==== | ====Options==== | ||
| - | * ''Simplifications'': one can specify additional simplifications that will be applied to each evaluated trace<sxh groovy; gutter: false> | + | * ''Simplifications'': one can specify additional simplifications that will be applied to each evaluated trace:<sxh groovy; gutter: false> |
| defineMatrices 'G_a', 'G5', Matrix1.matrix | defineMatrices 'G_a', 'G5', Matrix1.matrix | ||
| def expr = 'Tr[(p^a + k^a)*(p^b + k^b)*G_a*G_b*G_c*G_d]'.t | def expr = 'Tr[(p^a + k^a)*(p^b + k^b)*G_a*G_b*G_c*G_d]'.t | ||
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| </sxh> | </sxh> | ||
| + | * ''ExpandAndEliminate'': ''DiracTrace'' expands out products of sums containing traces of $\gamma$-matrices using [[ExpandAndEliminate]] transformation. One can replace it with another instance using ''%%DiractTrace[[ExpandAndEliminate: tr]]%%''. | ||
| - | ''DiracTrace'' expands out products of sums containing traces of $\gamma$-matrices and leaves unexpanded other parts of expressions: | + | * ''LeviCivitaSimplify'': When traces involve $\gamma_5$, ''DiracTrace'' uses [[LeviCivitaSimplify]] in for simplifying resulting expressions with Levi-Civita tensors. One can replace the default instance of [[LeviCivitaSimplify]] with another one using ''%%DiractTrace[[ExpandAndEliminate: tr]]%%''. |
| - | <sxh groovy; gutter: false> | ||
| - | defineMatrices 'G_a', 'G5', Matrix1.matrix | ||
| - | def expr = '(k_c+p_c)*(k_d+p_d) + Tr[(p^a + k^a)*(p^b + k^b)*G_a*G_b*G_c*G_d]'.t | ||
| - | println dTrace >> expr | ||
| - | </sxh> | ||
| - | <sxh plain; gutter: false> | ||
| - | > (k_c+p_c)*(k_d+p_d)+4*g_cd*p_b*p^b+4*k_b*k^b*g_cd+8*k^b*g_cd*p_b | ||
| - | </sxh> | ||
| ====See also==== | ====See also==== | ||
| * Related guides: [[documentation:guide:applying_and_manipulating_transformations]], [[documentation:guide:Setting up matrix objects]], [[documentation:guide:list_of_transformations]] | * 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 tutorials: [[documentation:tutorials:Compton scattering in QED]] | ||
| - | * Related transformations: [[documentation:ref:LeviCivitaSimplify]], [[documentation:ref:UnitaryTrace]] | + | * Related transformations: [[documentation:ref:DiracSimplify]], [[documentation:ref:DiracOrder]], [[documentation:ref:LeviCivitaSimplify]], [[documentation:ref:UnitaryTrace]] |
| - | * JavaDocs: [[http://api.redberry.cc/redberry/1.1.8/java-api//cc/redberry/physics/feyncalc/DiracTraceTransformation.html| DiracTraceTransformation]] | + | * JavaDocs: [[http://api.redberry.cc/redberry/1.1.9/java-api//cc/redberry/physics/feyncalc/DiracTraceTransformation.html| DiracTraceTransformation]] |
| * Source code: [[https://bitbucket.org/redberry/redberry/src/tip/physics/src/main/java/cc/redberry/physics/feyncalc/DiracTraceTransformation.java|DiracTraceTransformation.java]] | * Source code: [[https://bitbucket.org/redberry/redberry/src/tip/physics/src/main/java/cc/redberry/physics/feyncalc/DiracTraceTransformation.java|DiracTraceTransformation.java]] | ||
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