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====Description==== | ====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'', ''k2'' and ''k3'' with masses ''m1'', ''m2'' and ''m3'' and outcoming particles with momentums ''k4'' and ''k5'' with masses ''m4'' and ''m5''. | + | * ''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''. |
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</sxh> | </sxh> | ||
<sxh plain; gutter: false> | <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> | </sxh> | ||
---- | ---- | ||
Same when some particles are massless: | Same when some particles are massless: | ||
<sxh groovy; gutter: false> | <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 | println mandelstam | ||
</sxh> | </sxh> | ||
<sxh plain; gutter: false> | <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> | </sxh> | ||
====See also==== | ====See also==== | ||
* Related tutorials: [[documentation:tutorials:compton_scattering_in_scalar_qed]], [[documentation:tutorials:compton_scattering_in_qed]] | * Related tutorials: [[documentation:tutorials:compton_scattering_in_scalar_qed]], [[documentation:tutorials:compton_scattering_in_qed]] | ||
- | * JavaDocs: [[http://api.redberry.cc/redberry/1.1.8/java-api/cc/redberry/physics/feyncalc/FeynCalcUtils.html|FeynCalcUtils]] | + | * 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]] | * Source code: [[https://bitbucket.org/redberry/redberry/src/tip/physics/src/main/java/cc/redberry/physics/feyncalc/FeynCalcUtils.java|FeynCalcUtils.java]] | ||
+ |