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 documentation:ref:setmandelstam5 [2015/11/20 20:51]poslavskysv [Examples] documentation:ref:setmandelstam5 [2016/06/21 09:53] Line 1: Line 1: - ====== 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'',​ ''​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], 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:​ - - def mandelstam = setMandelstam5([k1_a:​ '​m1',​ k2_a: '​m2',​ k3_a: '​m3',​ k4_a: '​m4',​ k5_a: '​m5'​]) - 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 - > 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) - ​ - ---- - Same when some particles are massless: - - def mandelstam = setMandelstam5([k1_a:​ '​0',​ k2_a: '​m2',​ k3_a: '​m3',​ k4_a: '​0',​ k5_a: '​0'​ ]) - println mandelstam - ​ - - > 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) - ​ - - ====See also==== - * 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]] - * Source code: [[https://​bitbucket.org/​redberry/​redberry/​src/​tip/​physics/​src/​main/​java/​cc/​redberry/​physics/​feyncalc/​FeynCalcUtils.java|FeynCalcUtils.java]]