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what is this concept, what are we getting or achieving?? what is the meaning of wavefunction ψ becoming an operator, If that is so, then what are states described by, what do eigen values of psi ψ suggest??
You can construct a quantum field theory w/o referring to frequencies and w/o such an interpretation. Historically that was the way QFT was developed, but it's not a necessary ingredient for a construction.The place where "ψ(x) as operator" diverges from "ψ(x) as wavefunction" is the step where we reinterpret the negative frequency modes as positive energy antiparticles. ...
No, it's not the same theory.
Write down the Dirac-Lagrangian. In rel. QM the ψ(x) is a wave function, in QED ψ(x) becomes an operator acting on states. That's different.
In QM you have states |ψ> and wave functions ψ(x) = <x|ψ>.
In QED ψ(x) is itself an operator.
You can construct a quantum field theory w/o referring to frequencies and w/o such an interpretation. Historically that was the way QFT was developed, but it's not a necessary ingredient for a construction.
Aren't these two remarks referring to the same thing? I'd say yes, you can write down QFT without the negative-frequency reinterpretation, and historically it was done that way, but it turned out to be incorrect.In the case of the Dirac equation, the theory of a single particle is useful, but isn't completely sensible because of the kludge of the filled sea of antiparticles.
Yes, Srednicki was discussing a nonrelativistic QFT, for which the antiparticle issue doesn't arise.In the case of the non-relativistic Schroedinger equation for many identical particles, they are the same theory. The theory already works, but "second quantization" is a dual formulation that makes it easier to see some things.
You can construct a quantum field theory w/o referring to frequencies and w/o such an interpretation. Historically that was the way QFT was developed, but it's not a necessary ingredient for a construction.
In the case of the Dirac equation, the theory of a single particle is useful, but isn't completely sensible because of the kludge of the filled sea of antiparticles. There "second quantization" yields a different theory, of a field, which does work.
Aren't these two remarks referring to the same thing? I'd say yes, you can write down QFT without the negative-frequency reinterpretation, and historically it was done that way, but it turned out to be incorrect.
what is this concept, what are we getting or achieving?? what is the meaning of wavefunction ψ becoming an operator, If that is so, then what are states described by, what do eigen values of psi ψ suggest??
Second quantization was first developed by Jordan (1927) as an operator formalism for a system of n identical particles which automatically takes into account the symmetrization/antisymmetrization. Its aim was to act as a simpler replacement for the description by Slater determinants.First quantization is quantum mechanics where the total number of particles in the system is fixed... Second quantization is quantum mechanics where the total number of particles in the system changes.
what is this concept, what are we getting or achieving?? what is the meaning of wavefunction ψ becoming an operator, If that is so, then what are states described by, what do eigen values of psi ψ suggest??
I have to repeat what I've already said above several times. The field operator is not just an operator-valued interpretation of the original wavefunction. That's the way things started out, but it turned out to be wrong.we just quantize the corresponding fields, by applying the previous prescription (canonical quantization). That’s the meaning of interpreting a wave function as an operator-valued function of spacetime.