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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?

2 Replies

Take a look at FeynCalc:

https://feyncalc.github.io

Posted 5 years ago

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".

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