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MandelstamRelations

MandelstamRelations[{p1,p2,p3,p4,m1,m2,m3,m4}{s,t,u}]
gives a list of replacement rules expressing dot products of incoming 4vectors p1, p2 and outgoing 4vectors p3, p4 as Mandelstam invariants s, t, u, and masses m1, m2, m3, m4

Details and OptionsDetails and Options

  • MandelstamRelations can be used to rapidly generate a set of rules for the kinematics of scattering or 3-body decay processes.
  • MandelstamRelations effectively inverts the relations , , , and uses , , , to generate the set of rules.
  • The option Eliminate can be set to eliminate one of the invariants s, t, or u using the relationship .

ExamplesExamplesopen allclose all

Basic Examples  (3)Basic Examples  (3)

General kinematic relations for a scattering process:
    

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Eliminate Mandelstam :

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Kinematic relations for a three-body decay process (note the minus sign):
    

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Heavy particle kinematics. Two heavy particles of mass M at rest (velocity four-vectors v1 and v2 ) annihilating into two massless particles (momentum four-vecetors p3 and p4):

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