Difference between revisions of "Variables Used in Elastic Scattering"
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where represents the 4-Momentum Vector in the CM frame
and represents the 4-Momentum Vector in the initial Lab frame
where represents the 4-Momentum Vector in the final Lab frame
| Line 4: | Line 4: | ||
It was [[DV_Calculations_of_4-momentum_components#Equal_masses | further shown ]] that | It was [[DV_Calculations_of_4-momentum_components#Equal_masses | further shown ]] that | ||
<center><math>{\mathbf P^*}^2={\mathbf P}^2</math></center> | <center><math>{\mathbf P^*}^2={\mathbf P}^2</math></center> | ||
| − | <center>where <math>{\mathbf P^*}</math> represents the 4-Momentum Vector in the CM frame</center> | + | |
| − | <center> and <math>{\mathbf P}</math> represents the 4-Momentum Vector in the initial Lab frame</center> | + | <center>''where'' <math>{\mathbf P^*}</math> ''represents the 4-Momentum Vector in the CM frame''</center> |
| + | <center> ''and'' <math>{\mathbf P}</math> ''represents the 4-Momentum Vector in the initial Lab frame''</center> | ||
which can be expanded to | which can be expanded to | ||
| Line 11: | Line 12: | ||
<center><math>{\mathbf P^*}^2={\mathbf P}^2={\mathbf P^'}^2</math></center> | <center><math>{\mathbf P^*}^2={\mathbf P}^2={\mathbf P^'}^2</math></center> | ||
| − | <center>where <math>{\mathbf P^'}</math> represents the 4-Momentum Vector in the final Lab frame</center> | + | <center>''where'' <math>{\mathbf P^'}</math> ''represents the 4-Momentum Vector in the final Lab frame''</center> |
=Mandelstam Representation= | =Mandelstam Representation= | ||
[[File:Mandelstam.png | 400 px]] | [[File:Mandelstam.png | 400 px]] | ||
Revision as of 19:25, 31 January 2016
Lorentz Invariant Quantities
As was shown earlier the scalar product of a 4-Momentum vector with itself , , and the length of a 4-Momentum vector composed of 4-Momentum vectors, , are invariant quantities.
It was further shown that
which can be expanded to
Mandelstam Representation
