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- | ====== DiracOrder ====== | ||
- | ---- | ||
- | |||
- | ====Description==== | ||
- | |||
- | * ''%%DiracOrder%%'' brings all products of $\gamma$-matrices to alphabetical order | ||
- | |||
- | * By default ''%% DiracOrder%%'' works in $D = 4$; for arbitrary $D$ one can use option ''%% DiracOrder[[Dimension: D]]%%'' | ||
- | |||
- | * One can directly set trace of identity matrix (e.g. for dimensional regularisation): ''%% DiracOrder[[Dimension: D, TraceOfOne: 4]]%%'' | ||
- | |||
- | * By default ''DiracOrder'' uses notation ''G_m'' for $\gamma_m$ and ''G5'' for $\gamma_5$. ''%% DiracOrder[[Gamma: G, Gamma5: G5]]%%'' specifies the notation for $\gamma_m$, $\gamma_5$ and Levi-Civita tensor. | ||
- | |||
- | ====Examples==== | ||
- | ---- | ||
- | Order product of $\gamma$-matrices: | ||
- | <sxh groovy; gutter: true> | ||
- | defineMatrices 'G_a', 'G5', Matrix1.matrix | ||
- | def dOrder = DiracOrder | ||
- | println dOrder >> 'G_b*G_a'.t | ||
- | </sxh> | ||
- | <sxh plain; gutter: false> | ||
- | > 2*g_{ba}-G_{a}*G_{b} | ||
- | </sxh> | ||
- | <sxh groovy; gutter: true; first-line: 4> | ||
- | println dOrder >> 'G_d*G_c*G_b*G_a'.t | ||
- | </sxh> | ||
- | <sxh plain; gutter: false> | ||
- | > G_{a}*G_{b}*G_{c}*G_{d}-2*G_{c}*G_{d}*g_{ab}+2*G_{b}*G_{d}*g_{ac}-2*G_{b}*G_{c}*g_{ad} | ||
- | -2*G_{a}*G_{d}*g_{bc}+4*g_{ad}*g_{bc}+2*G_{a}*G_{c}*g_{bd}-4*g_{ac}*g_{bd} | ||
- | -2*G_{a}*G_{b}*g_{cd}+4*g_{ab}*g_{cd} | ||
- | </sxh> | ||
- | |||
- | All $\gamma_5$ will be shift right: | ||
- | <sxh groovy; gutter: true> | ||
- | defineMatrices 'G_a', 'G5', Matrix1.matrix | ||
- | def dOrder = DiracOrder | ||
- | println dOrder >> 'G5*G_b*G_a'.t | ||
- | </sxh> | ||
- | <sxh plain; gutter: false> | ||
- | > 2*G5*g_{ba}-G_{a}*G_{b}*G5 | ||
- | </sxh> | ||
- | |||
- | |||
- | ---- | ||
- | Use another notation for $\gamma$-matrices: | ||
- | <sxh groovy; gutter: true> | ||
- | defineMatrices 'F_a', 'F5', Matrix1.matrix | ||
- | def dOrder = DiracOrder[[Gamma: 'F_a', Gamma5: 'F5']] | ||
- | println dOrder >> 'F_b*F_a'.t | ||
- | </sxh> | ||
- | <sxh plain; gutter: false> | ||
- | > 2*g_{ba}-F_{a}*F_{b} | ||
- | </sxh> |