# How to implement time dependence in the DoFun package?

DoFun is a very usefull mathematica package that helps to write Dyson-Schwinger and FRG flow equations when these are to complex to write down by hand. You can download it here and read it's manual here.

With my basic experience with DoFun, I find myself unable to tackle properly out-of-equilibrium problems where Feynmann diagramms contain an integration over momentum and frequency.

I tried to consider the frequency as another index with

defineFieldsSpecific[{δϕ[momentum, frequency]}];


For simplicity I consider a scalar field that has no other indices. This failed because the

delta[frequency,ω_1,ω_2]


function does not handle negative indices as expected. For example, mathematica does not know that

delta[frequency,-\[\omega]_1,\[\omega]_2] = delta[frequency,\[\omega]_1,-\[\omega]_2]


and the function integrateDeltas can not handle expressions such as

delta[frequency,-\[\omega]_1,\[\omega]_2] ω_1 \\integrateDeltas


Any help on how to include frequency into my vertices would be welcome. Tips on how to use the delta function better or suggestions to solve my problem in a completely different way are welcome and needed.