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documentation:guide:list_of_transformations [2015/11/21 10:31] poslavskysv [Factor] |
documentation:guide:list_of_transformations [2015/11/21 11:03] poslavskysv |
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| - | ====== List of transformations ====== | + | ====== List of common transformations ====== |
| <html> | <html> | ||
| <div class="text-right" style="font-size: 15px; "> | <div class="text-right" style="font-size: 15px; "> | ||
| Line 91: | Line 91: | ||
| </sxh> | </sxh> | ||
| See [[documentation:ref:Differentiate]]. | See [[documentation:ref:Differentiate]]. | ||
| + | |||
| + | <html><hr style="border:dashed #555555; border-width:1px 0 0; height:0;"></html> | ||
| + | |||
| + | ====DiracSimplify==== | ||
| + | simplifies products of gamma matrices: | ||
| + | <sxh groovy; gutter: false> | ||
| + | defineMatrices 'G_a', 'G5', Matrix1.matrix | ||
| + | println DiracSimplify >> 'G5*G_a*G5*G_b*G^a*G^b'.t | ||
| + | </sxh> | ||
| + | <sxh plain; gutter: false> | ||
| + | > -8 | ||
| + | </sxh> | ||
| + | See [[documentation:ref:DiracSimpllify]]. | ||
| + | |||
| + | <html><hr style="border:dashed #555555; border-width:1px 0 0; height:0;"></html> | ||
| + | |||
| + | ====DiracOrder==== | ||
| + | order products of gamma matrices: | ||
| + | <sxh groovy; gutter: false> | ||
| + | defineMatrices 'G_a', 'G5', Matrix1.matrix | ||
| + | println DiracOrder >> 'G5*G_c*G_b*G_a'.t | ||
| + | </sxh> | ||
| + | <sxh plain; gutter: false> | ||
| + | > G_{a}*G_{b}*G_{c}*G5+2*G_{b}*G5*g_{ca}-2*G_{c}*G5*g_{ba}-2*G_{a}*G5*g_{cb} | ||
| + | </sxh> | ||
| + | See [[documentation:ref:DiracOrder]]. | ||
| <html><hr style="border:dashed #555555; border-width:1px 0 0; height:0;"></html> | <html><hr style="border:dashed #555555; border-width:1px 0 0; height:0;"></html> | ||
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| </sxh> | </sxh> | ||
| See [[documentation:ref:ExpandNumerator]]. | See [[documentation:ref:ExpandNumerator]]. | ||
| + | |||
| + | <html><hr style="border:dashed #555555; border-width:1px 0 0; height:0;"></html> | ||
| + | |||
| + | ====ExpandTensors==== | ||
| + | expands only indexed parts: | ||
| + | <sxh groovy; gutter: false> | ||
| + | println ExpandTensors >> '(a + b)**2*(A_a + B_a)*(A^a + B^a)'.t | ||
| + | </sxh> | ||
| + | <sxh plain; gutter: false> | ||
| + | > (a+b)**2*A^{a}*A_{a}+2*(a+b)**2*A^{a}*B_{a}+(a+b)**2*B^{a}*B_{a} | ||
| + | </sxh> | ||
| + | See [[documentation:ref:ExpandTensors]]. | ||
| <html><hr style="border:dashed #555555; border-width:1px 0 0; height:0;"></html> | <html><hr style="border:dashed #555555; border-width:1px 0 0; height:0;"></html> | ||
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| <html><hr style="border:dashed #555555; border-width:1px 0 0; height:0;"></html> | <html><hr style="border:dashed #555555; border-width:1px 0 0; height:0;"></html> | ||
| + | ====SpinorsSimplify==== | ||
| + | simplifies Dirac spinors: | ||
| + | <sxh groovy; gutter: false> | ||
| + | defineMatrices 'G_a', 'G5', Matrix1.matrix, 'cu', Matrix1.covector | ||
| + | def sSimplify = SpinorsSimplify[[uBar: 'cu', Momentum: 'p_a', Mass: 'm']] | ||
| + | println sSimplify >> 'cu*G^a*p_a'.t | ||
| + | </sxh> | ||
| + | <sxh plain; gutter: false> | ||
| + | > -m*cu*G_{b}+2*cu*p_{b} | ||
| + | </sxh> | ||
| + | See [[documentation:ref:SpinorsSimplify]]. | ||
| + | |||
| + | <html><hr style="border:dashed #555555; border-width:1px 0 0; height:0;"></html> | ||
| + | |||
| ====Symmetrize==== | ====Symmetrize==== | ||
| gives a symmetrization of tensor with respect to specified indices under the specified symmetries: | gives a symmetrization of tensor with respect to specified indices under the specified symmetries: | ||