====== DiracSimplify ======
----

====Description====

  * ''%%DiracSimplify%%'' simplifies products of gamma matrices

  * By default ''%%DiracSimplify%%'' works in $D = 4$; for arbitrary $D$ one can use option ''%%DiracSimplify[[Dimension: D]]%%''

  * One can directly set trace of identity matrix (e.g. for dimensional regularisation): ''%%DiracSimplify[[Dimension: D, TraceOfOne: 4]]%%''

  * By default ''DiracSimplify'' uses notation ''G_m'' for $\gamma_m$ and ''G5'' for $\gamma_5$.  ''%%DiracSimplify[G, G5]%%'' or ''%% DiracSimplify[[Gamma: G, Gamma5: G5]]%%'' specifies the notation for $\gamma_m$ and $\gamma_5$.

  * ''%% DiracSimplify[[Simplifications: rules]]%%'' will apply additional simplification ''rules'' to each processed product of gammas


====Examples====
----
Simplify different expressions:
<sxh groovy; gutter: true>
defineMatrices 'G_a', 'G5', Matrix1.matrix
def dSimplify = DiracSimplify
println dSimplify >> 'G_a*G^a'.t
</sxh>
<sxh plain; gutter: false>
   > 4
</sxh>
<sxh groovy; gutter: true; first-line: 4>
println dSimplify >> 'G_a*G_b*G^a'.t
</sxh>
<sxh plain; gutter: false>
   > -2*G_{b}
</sxh>
<sxh groovy; gutter: true; first-line: 5>
println dSimplify >> 'G_a*G_b*G^a*G^b'.t
</sxh>
<sxh plain; gutter: false>
   > -8
</sxh>
<sxh groovy; gutter: true; first-line: 6>
println dSimplify >> 'G5*G_a*G_b*G^a*G^b*G5*G5'.t
</sxh>
<sxh plain; gutter: false>
   > -8*G5
</sxh>
<sxh groovy; gutter: true; first-line: 7>
println dSimplify >> 'G5*G_a*G_b*G^a*G5*G5'.t
</sxh>
<sxh plain; gutter: false>
   > 2*G_{b}
</sxh>

----
Simplify in different dimensions:
<sxh groovy; gutter: true>
defineMatrices 'G_a', 'G5', Matrix1.matrix
def dSimplify = DiracSimplify[[Dimension: 'D']]
println dSimplify >> 'G_a*G^a'.t
</sxh>
<sxh plain; gutter: false>
   > D
</sxh>
<sxh groovy; gutter: true; first-line: 4>
println dSimplify >> 'G_a*G_b*G^a'.t
</sxh>
<sxh plain; gutter: false>
   > -(-2+D)*G_{b}
</sxh>

----
Specify additional simplifications:
<sxh groovy; gutter: true>
defineMatrices 'G_a', 'G5', Matrix1.matrix
def dSimplify = DiracSimplify[[Simplifications: 'p_a*k^a = s'.t]]
println dSimplify >> 'p^b*k^c*G_a*G_b*G_c*G^a'.t
</sxh>
<sxh plain; gutter: false>
   > 4*s
</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 QED]]
  * Related transformations: [[documentation:ref:DiracTrace]], [[documentation:ref:spinorssimplify]], [[documentation:ref:DiracOrder]],  [[documentation:ref:LeviCivitaSimplify]], [[documentation:ref:UnitarySimplify]], [[documentation:ref:UnitaryTrace]]
  * JavaDocs: [[http://api.redberry.cc/redberry/1.1.9/java-api//cc/redberry/physics/feyncalc/DiracSimplifyTransformation.html| DiracSimplifyTransformation]]
  * Source code: [[https://bitbucket.org/redberry/redberry/src/tip/physics/src/main/java/cc/redberry/physics/feyncalc/DiracSimplifyTransformation.java|DiracSimplifyTransformation.java]]