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--- documentation:ref:setmandelstam5 [2015/11/20 20:49]
poslavskysv created
+++ documentation:ref:setmandelstam5 [2015/11/20 20:51]
poslavskysv [See also]
@@ Line 23: / Line 23: @@
 </sxh>
 <sxh plain; gutter: false>
-  > k1_{a}*k1^{a} = m1**2
+ > k1_{a}*k1^{a} = m1**2
-  > k2_{a}*k2^{a} = m2**2
+ > k2_{a}*k2^{a} = m2**2
-  > k3_{a}*k3^{a} = m3**2
+ > k3_{a}*k3^{a} = m3**2
-  > k4_{a}*k4^{a} = m4**2
+ > k4_{a}*k4^{a} = m4**2
-  > 2*k1_{a}*k2^{a} = s-m2**2-m1**2
+ > k5_{a}*k5^{a} = m5**2
-  > 2*k4^{a}*k3_{a} = s-m3**2-m4**2
+ > k2^{a}*k1_{a} = (1/2)*(-m1**2-m2**2+s)
-  > -2*k3^{a}*k1_{a} = t-m3**2-m1**2
+ > k3^{a}*k1_{a} = (1/2)*(m1**2-t1+m3**2)
-  > -2*k4^{a}*k2_{a} = t-m4**2-m2**2
+ > k1_{a}*k4^{a} = (1/2)*(m4**2+m1**2-t2)
-  > -2*k4^{a}*k1_{a} = -m4**2-m1**2+u
+ > k1_{a}*k5^{a} = (1/2)*(-m4**2-m1**2+t2+t1-m2**2-m3**2+s)
-  > -2*k3^{a}*k2_{a} = -m3**2-m2**2+u
+ > 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 = setMandelstam([k1_a: '0', k2_a: 'm2', k3_a: 'm3', k4_a: '0'])
+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
+ > k1_{a}*k1^{a} = 0
-   > k2_{a}*k2^{a} = m2**2
+ > k2_{a}*k2^{a} = m2**2
-   > k3_{a}*k3^{a} = m3**2
+ > k3_{a}*k3^{a} = m3**2
-   > k4_{a}*k4^{a} = 0
+ > k4_{a}*k4^{a} = 0
-   > 2*k2^{a}*k1_{a} = -m2**2+s
+ > k5_{a}*k5^{a} = 0
-   > 2*k4^{a}*k3_{a} = -m3**2+s
+ > k2^{a}*k1_{a} = (1/2)*(s-m2**2)
-   > -2*k3^{a}*k1_{a} = -m3**2+t
+ > k1_{a}*k3^{a} = (1/2)*(-t1+m3**2)
-   > -2*k4^{a}*k2_{a} = t-m2**2
+ > k4^{a}*k1_{a} = -(1/2)*t2
-   > -2*k4^{a}*k1_{a} = u
+ > k1_{a}*k5^{a} = (1/2)*(t1+s-m2**2+t2-m3**2)
-   > -2*k2_{a}*k3^{a} = -m3**2+u-m2**2
+ > k2_{a}*k3^{a} = (1/2)*(-u1+m2**2+m3**2)
-</sxh>
+ > k4^{a}*k2_{a} = (1/2)*(-u2+m2**2)
-----
+ > k2_{a}*k5^{a} = (1/2)*(u1+u2+s-m2**2-m3**2)
-Specify custom notation for Mandelstam variables:
+ > k4^{a}*k3_{a} = (1/2)*(-t1-u1-u2-s-t2+m3**2+2*m2**2)
-<sxh groovy; gutter: false>
+ > k3_{a}*k5^{a} = (1/2)*(u2+s-m2**2+t2-m3**2)
-def mandelstam = setMandelstam(
+ > k4_{a}*k5^{a} = (1/2)*(t1+u1+s-m2**2-m3**2)
-        [k1_a: 'm1', k2_a: 'm2', k3_a: 'm3', k4_a: 'm4'],
-        'hS', 'hT', 'hU')
-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
-  > 2*k2^{a}*k1_{a} = -m1**2+hS-m2**2
-  > 2*k3_{a}*k4^{a} = -m3**2+hS-m4**2
-  > -2*k3^{a}*k1_{a} = -m3**2-m1**2+hT
-  > -2*k2_{a}*k4^{a} = hT-m4**2-m2**2
-  > -2*k1_{a}*k4^{a} = -m1**2+hU-m4**2
-  > -2*k2_{a}*k3^{a} = -m3**2+hU-m2**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/1.1.8/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]]