Canonical quantization of vector fields?

[Jay R. Yablon]

I am trying to find the right name for the commutation equation
(d=partial derivative):

d^uA^v = i[p^u,A^v] (1)

for a vector field A^v, where p^u is a four-momentum operator. This
relates to the Hamiltonian equation of motion:

d^0A^v = i[H,A^v] (2).

What names / verbiage does one usually use to talk about (1)? Can one
say that equation (1) is part of how we canonically quantize A^v?

Again, I am just looking for the best language with which to speak about
equation (1).

Thanks,

Jay
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[Vladimir Kalitvianski]

They are called (four-dimensional) equations of motion, kind of
generalization of the Heisenberg equation to the spatial components.

[Jay R. Yablon]

"Vladimir Kalitvianski" wrote in message
news:11311150.3098.1337243893672.JavaMail.geo-discussion-forums@yncd3...

They are called (four-dimensional) equations of motion, kind of
generalization of the Heisenberg equation to the spatial components.

Jay R. Yablon now writes:

So in:

d^uA^v = i[p^u,A^v] with u,v=0,1,2,3

is the p^u = (p^0, p^1, p^2, p^3) a sort of hybrid four-vector, in which the
p^0 = H component is the Hamiltonian and the p^1, p^2, p^3 spatial components
are ordinary three-momentum?

Jay