# Working with 4-vectors?

Posted 5 years ago
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 Define an expression like: $\chi\,=\,C_{p1}\,\left[ h\,e^{- i\,p1.\,x}\,\, +\,\,h^{\dagger}\,e^{+i\,p1\,.\,x}\right]$where $p1$ and $x$ are four-vectors; $C_{p1} = \ \frac{1}{\sqrt{(2 \pi)^3} \sqrt{2 \omega\,(p1,\ m)}}$, and $x\ .\ p1\ =\omega(p_1,m)\,t\ - {\vec p1} {\vec x}$ How does one teach Mathematica to do things like $\chi \cdot \chi\,$, $\nabla \chi$, $\partial_{t}\ \chi$ etc. but not have to explicitly have to type the full form of the four vectors - in the subsequent input and results of evaluations?
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Posted 5 years ago
 Take a look at FeynCalc:https://feyncalc.github.io
 Thank you David Reiss.In FeynCalc, I would like to define a scalar operator as $\chi$ = Integrate[C[p1] (h[p1] e$^{-I p1 x}$ + h$^{\dagger}$[p1] e$^{I p1 x}$, d$\vec p1$] i.e. the integration is over ${\vec p1}$ (3-vector). $p1$ and $x$ are four vectors, given by $p1$ = ( $\omega$ [p1, m]*t, vec{p1}) and $x$ = (t, vec{x}). Tried the following $p1$ :=FourVector[ $\omega$[p1,m], m] x := FourVector[t,r], $\chi$ := Integrate[C[p1] (h[p1]E$^{-I p1 x}$ + h^${\dagger}$[p1]E^${I p1 x}$, {$p1$,-Infinity,Infinity}];If I try any calculation like FourDivergence[ $\chi$], it either returns the input FourDivergence[ full form of \chi], or just complains "Recursion limit reached". What am I doing incorrectly? Note that the $\chi$ has been rendered in Mathematica in the above input text, by "Esc":\chi":"Esc".