Editing Mandelstam variables (section)

{{Short description|Variables used in scattering processes}}
{{for|other articles using the same surname|Mandelstam}}
[[Image:Mandelstam.svg|right|thumb|220px|In this diagram, two particles come in with momenta p<sub>1</sub> and p<sub>2</sub>, they interact in some fashion, and then two particles with different momentum (p<sub>3</sub> and p<sub>4</sub>) leave.]]
In [[theoretical physics]], the '''Mandelstam variables''' are numerical quantities that encode the [[energy]], [[momentum]], and angles of particles in a scattering process in a [[Lorentz symmetry|Lorentz-invariant]] fashion. They are used for scattering processes of two particles to two particles. The Mandelstam variables were first introduced by physicist [[Stanley Mandelstam]] in 1958.

If the [[Minkowski metric]] is chosen to be <math>\mathrm{diag}(1, -1,-1,-1)</math>, the Mandelstam variables <math>s,t,u</math> are then defined by
:*<math>s=(p_1+p_2)^2 c^2 =(p_3+p_4)^2 c^2</math>
:*<math>t=(p_1-p_3)^2 c^2 =(p_4-p_2)^2 c^2</math>
:*<math>u=(p_1-p_4)^2 c^2 =(p_3-p_2)^2 c^2</math>,
where ''p''<sub>1</sub> and ''p''<sub>2</sub> are the [[four-momentum|four-momenta]] of the incoming particles and ''p''<sub>3</sub> and ''p''<sub>4</sub> are the four-momenta of the outgoing particles.

<math>s</math> is also known as the square of the center-of-mass energy ([[invariant mass]]) and <math>t</math> as the square of the [[four-momentum]] transfer.