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?
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”.