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| - | ====== 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: | ||
| - | <sxh groovy; gutter: true> | ||
| - | defineMatrices 'G_a', 'G5', Matrix1.matrix | ||
| - | def dSimplify = DiracSimplify | ||
| - | println dSimplify >> 'G_a*G^a'.t | ||
| - | </sxh> | ||
| - | <sxh plain; gutter: false> | ||
| - | > 4 | ||
| - | </sxh> | ||
| - | <sxh groovy; gutter: true; first-line: 4> | ||
| - | println dSimplify >> 'G_a*G_b*G^a'.t | ||
| - | </sxh> | ||
| - | <sxh plain; gutter: false> | ||
| - | > -2*G_{b} | ||
| - | </sxh> | ||
| - | <sxh groovy; gutter: true; first-line: 5> | ||
| - | println dSimplify >> 'G_a*G_b*G^a*G^b'.t | ||
| - | </sxh> | ||
| - | <sxh plain; gutter: false> | ||
| - | > -8 | ||
| - | </sxh> | ||
| - | <sxh groovy; gutter: true; first-line: 6> | ||
| - | println dSimplify >> 'G5*G_a*G_b*G^a*G^b*G5*G5'.t | ||
| - | </sxh> | ||
| - | <sxh plain; gutter: false> | ||
| - | > -8*G5 | ||
| - | </sxh> | ||
| - | <sxh groovy; gutter: true; first-line: 7> | ||
| - | println dSimplify >> 'G5*G_a*G_b*G^a*G5*G5'.t | ||
| - | </sxh> | ||
| - | <sxh plain; gutter: false> | ||
| - | > 2*G_{b} | ||
| - | </sxh> | ||
| - | |||
| - | ---- | ||
| - | Simplify in different dimensions: | ||
| - | <sxh groovy; gutter: true> | ||
| - | defineMatrices 'G_a', 'G5', Matrix1.matrix | ||
| - | def dSimplify = DiracSimplify[[Dimension: 'D']] | ||
| - | println dSimplify >> 'G_a*G^a'.t | ||
| - | </sxh> | ||
| - | <sxh plain; gutter: false> | ||
| - | > D | ||
| - | </sxh> | ||
| - | <sxh groovy; gutter: true; first-line: 4> | ||
| - | println dSimplify >> 'G_a*G_b*G^a'.t | ||
| - | </sxh> | ||
| - | <sxh plain; gutter: false> | ||
| - | > -(-2+D)*G_{b} | ||
| - | </sxh> | ||
| - | |||
| - | ---- | ||
| - | Specify additional simplifications: | ||
| - | <sxh groovy; gutter: true> | ||
| - | 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 | ||
| - | </sxh> | ||
| - | <sxh plain; gutter: false> | ||
| - | > 4*s | ||
| - | </sxh> | ||
| - | ====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]] | ||