I'm a little confused in the allocation of t,x,y,z dependence between the states and fields in all the different pictures.
In QM, we had a state ψ and an operator A. In the SP, ψ is a function of t and A isn't. In the HP, A is a function of t and ψ isn't.
In QFT, we have a state ψ and an operator A. But we also give ourselves three new dependent variables for our system to do whatever it wants with; x,y,z. I don't see a reason why we don't have xyzHeisenberg pictures and xyzSchrodinger pictures. Not necessarily saying they would be useful, but their complete lack of mention in P&S, Zee, Srednicki, Zuber etc have me puzzled. Can't we pick between an operator relation of any of these?
A(0)ψ(t,x,y,z) --- A(x,y,z)ψ(t) --- A(t)ψ(x,y,z) --- A(t,x,y,z)ψ(0)
Also, if anybody has a resource that talks about this, I'd like to read it.
In QM, we had a state ψ and an operator A. In the SP, ψ is a function of t and A isn't. In the HP, A is a function of t and ψ isn't.
In QFT, we have a state ψ and an operator A. But we also give ourselves three new dependent variables for our system to do whatever it wants with; x,y,z. I don't see a reason why we don't have xyzHeisenberg pictures and xyzSchrodinger pictures. Not necessarily saying they would be useful, but their complete lack of mention in P&S, Zee, Srednicki, Zuber etc have me puzzled. Can't we pick between an operator relation of any of these?
A(0)ψ(t,x,y,z) --- A(x,y,z)ψ(t) --- A(t)ψ(x,y,z) --- A(t,x,y,z)ψ(0)
Also, if anybody has a resource that talks about this, I'd like to read it.
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