Differences

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--- documentation:ref:diractrace [2015/11/20 19:18]
poslavskysv [Options]
+++ documentation:ref:diractrace [2015/11/21 12:33] (current)
@@ Line 106: / Line 106: @@
 ----
-''DiracTrace'' expands out products of sums containing traces of $\gamma$-matrices and leaves unexpanded other parts of expressions:
+Use another notation for gamma matrices:
 <sxh groovy; gutter: false>
-defineMatrices 'G_a', 'G5', Matrix1.matrix
+defineMatrices 'F_\\mu', 'F5', Matrix2.matrix
-def expr = '(k_c+p_c)*(k_d+p_d) + Tr[(p^a + k^a)*(p^b + k^b)*G_a*G_b*G_c*G_d]'.t
+def dTrace = DiracTrace[[Gamma: 'F_\\mu', Gamma5: 'F5', LeviCivita: 'Eps_{\\mu\\nu\\alpha\\beta}']]
-println dTrace >> expr
+println dTrace >> 'Tr[F_\\mu*F_\\nu*F_\\alpha*F_\\beta * F5]'.t
 </sxh>
 <sxh plain; gutter: false>
-   > (k_c+p_c)*(k_d+p_d)+4*g_cd*p_b*p^b+4*k_b*k^b*g_cd+8*k^b*g_cd*p_b
+   > -4*I*Eps_{\mu\nu\alpha\beta}
 </sxh>
 ====Options====
-  * ''Simplifications''. One can specify additional simplifications that will be applied to each evaluated trace
+  * ''Simplifications'': one can specify additional simplifications that will be applied to each evaluated trace:<sxh groovy; gutter: false>
+defineMatrices 'G_a', 'G5', Matrix1.matrix
+def expr = 'Tr[(p^a + k^a)*(p^b + k^b)*G_a*G_b*G_c*G_d]'.t
+def mandelstam = setMandelstam([k_a: '0', p_a: '0', q_a: 'm', r_a: 'm'], 's', 't', 'u')
+println DiracTrace[[Simplifications: mandelstam]] >> expr
+</sxh><sxh plain; gutter: false>
+   > 4*s*g_{cd}
+</sxh>which is same as<sxh groovy; gutter: false>
+println( (DiracTrace & mandelstam) >> expr )
+</sxh><sxh plain; gutter: false>
+   > 4*s*g_{cd}
+</sxh>
+  * ''ExpandAndEliminate'': ''DiracTrace'' expands out products of sums containing traces of $\gamma$-matrices using [[ExpandAndEliminate]] transformation. One can replace it with another instance using ''%%DiractTrace[[ExpandAndEliminate: tr]]%%''.
+  * ''LeviCivitaSimplify'': When traces involve $\gamma_5$, ''DiracTrace'' uses [[LeviCivitaSimplify]] in for simplifying resulting expressions with Levi-Civita tensors. One can replace the default instance of [[LeviCivitaSimplify]] with another one using ''%%DiractTrace[[ExpandAndEliminate: tr]]%%''.
 ====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:LeviCivitaSimplify]], [[documentation:ref:UnitaryTrace]]
+  * Related transformations: [[documentation:ref:DiracSimplify]], [[documentation:ref:DiracOrder]],  [[documentation:ref:LeviCivitaSimplify]], [[documentation:ref:UnitaryTrace]]
-  * JavaDocs: [[http://api.redberry.cc/redberry/1.1.8/java-api//cc/redberry/physics/feyncalc/DiracTraceTransformation.html| DiracTraceTransformation]]
+  * JavaDocs: [[http://api.redberry.cc/redberry/1.1.9/java-api//cc/redberry/physics/feyncalc/DiracTraceTransformation.html| DiracTraceTransformation]]
   * Source code: [[https://bitbucket.org/redberry/redberry/src/tip/physics/src/main/java/cc/redberry/physics/feyncalc/DiracTraceTransformation.java|DiracTraceTransformation.java]]