Editing Mandelstam variables (section)

==Feynman diagrams==
The letters ''s,t,u'' are also used in the terms '''s-channel''' (timelike channel), '''t-channel''', and '''u-channel''' (both spacelike channels). These channels represent different [[Feynman diagram]]s or different possible scattering events where the interaction involves the exchange of an intermediate particle whose squared four-momentum equals ''s,t,u'', respectively.

::{|cellpadding="10"
|[[Image:S-channel.svg|150px]]
|[[Image:T-channel.svg|150px]]
|[[Image:U-channel.svg|150px]]
|-
|align="center"|'''s-channel'''
|align="center"|'''t-channel'''
|align="center"|'''u-channel'''
|}
For example, the s-channel corresponds to the particles 1,2 joining into an intermediate particle that eventually splits into 3,4: {{citation needed span|the s-channel is the only way that [[resonance (quantum field theory)|resonances]] and new [[unstable particle]]s may be discovered provided their lifetimes are long enough that they are directly detectable.|date=July 2014|reason=See 's-channel discovery' discussion on talk page}} The t-channel represents the process in which the particle 1 emits the intermediate particle and becomes the final particle 3, while the particle 2 absorbs the intermediate particle and becomes 4. The u-channel is the t-channel with the role of the particles 3,4 interchanged.

When evaluating a Feynman amplitude one often finds scalar products of the external four momenta. One can use the Mandelstam variables to simplify these:

<math>\left(p_1c\right)\cdot\left(p_2c\right) = \frac{1}{2}\left(s - \left(m_1c^2\right)^2 - \left(m_2c^2\right)^2\right)</math>  

<math>\left(p_1c\right)\cdot\left(p_3c\right) = \frac{1}{2}\left(\left(m_1c^2\right)^2 + \left(m_3c^2\right)^2 - t\right)</math>

<math>\left(p_1c\right)\cdot\left(p_4c\right) = \frac{1}{2}\left(\left(m_1c^2\right)^2 + \left(m_4c^2\right)^2 - u\right)</math>

Where <math>m_i</math> is the mass of the particle with corresponding momentum <math>p_i</math>.