====== setMandelstam5 ======
----
====Description====

  * ''setMandelstam5([k1:m1, k2:m2, k3:m3, k4:m4, k5:m5])''  generates a list of generalised Mandelstam and mass shell substitutions for incoming particles with momentums ''k1'' and ''k2'' with masses ''m1'' and ''m2'' and outcoming particles with momentums ''k3'', ''k4'' and ''k5'' with masses ''m3'', ''m4'' and ''m5''.


  * ''setMandelstam5([k1:m1, k2:m2, k3:m3, k4:m4, k5:m5], s, t1, t2, u1, u2)''  generates a list of Mandelstam substitutions with specified notation for generalised Mandelstam s, t1, t2, u1 and u2 variables.

  * ''setMandelstam5'' uses the following definition of Mandelstam variables:
\begin{gather*}
s = (p_1 + p_2)^2\\
t_1 = (p_1 - p_3)^2 \\
t_2 = (p_1 - p_4)^2 \\
u_1 = (p_2 - p_3)^2 \\
u_2 = (p_2 - p_4)^2 \\
\end{gather*}
====Examples====
Generate a list of Mandelstam and mass shell substitutions:
<sxh groovy; gutter: false>
def mandelstam = setMandelstam5([k1_a: 'm1', k2_a: 'm2', k3_a: 'm3', k4_a: 'm4', k5_a: 'm5'])
println mandelstam
</sxh>
<sxh plain; gutter: false>
 > k1_{a}*k1^{a} = m1**2
 > k2_{a}*k2^{a} = m2**2
 > k3_{a}*k3^{a} = m3**2
 > k4_{a}*k4^{a} = m4**2
 > k5_{a}*k5^{a} = m5**2
 > k2^{a}*k1_{a} = (1/2)*(-m1**2-m2**2+s)
 > k3^{a}*k1_{a} = (1/2)*(m1**2-t1+m3**2)
 > k1_{a}*k4^{a} = (1/2)*(m4**2+m1**2-t2)
 > k1_{a}*k5^{a} = (1/2)*(-m4**2-m1**2+t2+t1-m2**2-m3**2+s)
 > k2_{a}*k3^{a} = (1/2)*(-u1+m2**2+m3**2)
 > k2_{a}*k4^{a} = (1/2)*(m4**2-u2+m2**2)
 > k2_{a}*k5^{a} = (1/2)*(-m4**2-m1**2+u1+u2-m2**2-m3**2+s)
 > k3_{a}*k4^{a} = (1/2)*(m4**2+m5**2+2*m1**2-t2-u1-t1-u2+m3**2-s+2*m2**2)
 > k3_{a}*k5^{a} = (1/2)*(-m4**2-m1**2-m5**2+t2+u2-m2**2-m3**2+s)
 > k5^{a}*k4_{a} = (1/2)*(-m4**2-m1**2-m5**2+u1+t1-m2**2-m3**2+s)
</sxh>
----
Same when some particles are massless:
<sxh groovy; gutter: false>
def mandelstam = setMandelstam5([k1_a: '0', k2_a: 'm2', k3_a: 'm3', k4_a: '0', k5_a: '0' ])
println mandelstam
</sxh>
<sxh plain; gutter: false>
 > k1_{a}*k1^{a} = 0
 > k2_{a}*k2^{a} = m2**2
 > k3_{a}*k3^{a} = m3**2
 > k4_{a}*k4^{a} = 0
 > k5_{a}*k5^{a} = 0
 > k2^{a}*k1_{a} = (1/2)*(s-m2**2)
 > k1_{a}*k3^{a} = (1/2)*(-t1+m3**2)
 > k4^{a}*k1_{a} = -(1/2)*t2
 > k1_{a}*k5^{a} = (1/2)*(t1+s-m2**2+t2-m3**2)
 > k2_{a}*k3^{a} = (1/2)*(-u1+m2**2+m3**2)
 > k4^{a}*k2_{a} = (1/2)*(-u2+m2**2)
 > k2_{a}*k5^{a} = (1/2)*(u1+u2+s-m2**2-m3**2)
 > k4^{a}*k3_{a} = (1/2)*(-t1-u1-u2-s-t2+m3**2+2*m2**2)
 > k3_{a}*k5^{a} = (1/2)*(u2+s-m2**2+t2-m3**2)
 > k4_{a}*k5^{a} = (1/2)*(t1+u1+s-m2**2-m3**2)
</sxh>

====See also====
  * Related tutorials: [[documentation:tutorials:compton_scattering_in_scalar_qed]], [[documentation:tutorials:compton_scattering_in_qed]]
  * Related functions: [[documentation:ref:setmandelstam]]
  * JavaDocs: [[http://api.redberry.cc/redberry/1.1.9/java-api/cc/redberry/physics/feyncalc/FeynCalcUtils.html|FeynCalcUtils]]
  * Source code: [[https://bitbucket.org/redberry/redberry/src/tip/physics/src/main/java/cc/redberry/physics/feyncalc/FeynCalcUtils.java|FeynCalcUtils.java]]