Can the equations for two retarded potentials satisfy the Lorenz condition?

[kkabi_seo]

I wonder these equations can satisfy the Lorenz condition??

I mean.. how above equations can satisfy the divergence A + 1/c^2 dϕ/dt =0.

 

[rrogers]

I think the direct equation you want is div(curl(V))=0; for instance, https://math.stackexchange.com/ques...nation-for-operatornamediv-operatornamecurl-f
Now reasoning backward's from div(V)= 0 to integration and proving the conditions for V=curl(R) escapes me right now. Although I think that moving to Tensors and/or differential forms, might work. I also think that this is equivalent to conditions on ρ(x,t), J(x,t); i.e a space-time current/flow flow. If nobody else answers I will look it up.
Old with memory even poorer than when I was younger :)
Ray

 

[Meir Achuz]

The Lorenz condition is used in the derivation of the two retarded potentials so they must satisfy it.
Proving that it does, starting with those integrals, is tricky because it is difficult to differentiate the retarded time.