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 documentation:ref:setmandelstam5 [2015/11/20 20:49]poslavskysv created documentation:ref:setmandelstam5 [2016/06/21 09:53] (current) 2015/11/20 20:51 poslavskysv [See also] 2015/11/20 20:51 poslavskysv [Examples] 2015/11/20 20:49 poslavskysv created Next revision Previous revision 2015/11/20 20:51 poslavskysv [See also] 2015/11/20 20:51 poslavskysv [Examples] 2015/11/20 20:49 poslavskysv created Line 3: Line 3: ====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''​. Line 23: Line 23: - ​> 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) ​ ---- ---- Same when some particles are massless: Same when some particles are massless: - 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 - > 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) - ​ + > ​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) - + > ​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 + - ​ + - + - > 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 + ​ ====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]] +