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documentation:guide:list_of_transformations [2015/11/21 10:31] poslavskysv [Factor] |
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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; "> | ||
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</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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eliminates metric tensors and kronecker deltas: | eliminates metric tensors and kronecker deltas: | ||
<sxh groovy; gutter: false> | <sxh groovy; gutter: false> | ||
- | println EliminateMetric >> 'g_mn*A^m + d_n^a*B_a'.t | + | println EliminateMetrics >> 'g_mn*A^m + d_n^a*B_a'.t |
</sxh> | </sxh> | ||
<sxh plain; gutter: false> | <sxh plain; gutter: false> | ||
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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: | ||
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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> | ||
+ |