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| + | ====== UnitarySimplify ====== | ||
| + | ---- | ||
| + | ====Description==== | ||
| + | * ''%% UnitarySimplify%%'' simplifies combinations of SU(N) matrices and SU(N) structural and $d$-constants in expression. | ||
| + | |||
| + | |||
| + | * By default ''UnitarySimplify'' uses notation ''T_A'' for SU(N) matrices, ''f_ABC'' for SU(N) structural constants, ''d_ABC'' for $d$-constatnts and ''N'' for dimension. | ||
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| + | * ''%% UnitarySimplify[[Matrix: T, f: f, d: d, N:n]]%%'' specifies the notation for SU(N) matrices, structural constants, $d$-constants and dimension . | ||
| + | ====Examples==== | ||
| + | Simplify product of SU(N) matrices: | ||
| + | <sxh groovy; gutter: true> | ||
| + | defineMatrices 'T_A', Matrix2.matrix | ||
| + | println UnitarySimplify[[Matrix: 'T_A']] >> 'T_A*T^A'.t | ||
| + | </sxh> | ||
| + | <sxh plain; gutter: false> | ||
| + | > (1/2)*(N**2-1)*N**(-1) | ||
| + | </sxh> | ||
| + | <sxh groovy; gutter: true; first-line: 3> | ||
| + | println UnitarySimplify[[Matrix: 'T_A']] >> 'T_A*T_B*T^A'.t | ||
| + | </sxh> | ||
| + | <sxh plain; gutter: false> | ||
| + | > -(1/2)*N**(-1)*T_{B} | ||
| + | </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 QCD]] | ||
| + | * Related transformations: [[documentation:ref:unitarytrace]], [[documentation:ref:diractrace]] | ||
| + | * JavaDocs: [[http://api.redberry.cc/redberry/1.1.9/java-api//cc/redberry/physics/feyncalc/UnitarySimplifyTransformation.html| UnitarySimplifyTransformation]] | ||
| + | * Source code: [[https://bitbucket.org/redberry/redberry/src/tip/physics/src/main/java/cc/redberry/physics/feyncalc/UnitarySimplifyTransformation.java|UnitarySimplifyTransformation.java]] | ||