Schrodinger equation in quantum field theory

[accdd]

What is the Schrödinger equation in QFT? is it the nonrelativistic approximation of a Klein-Gordon scalar field? or Is there more?
I have read that the Schrödinger equation describes a QFT in 0 dimensions.
I accept every answer

 

[malawi_glenn]

I have read that the Schrödinger equation describes a QFT in 0 dimensions.

where?

 

[haushofer]

What is the Schrödinger equation in QFT? is it the nonrelativistic approximation of a Klein-Gordon scalar field? or Is there more?
I have read that the Schrödinger equation describes a QFT in 0 dimensions.
I accept every answer

It depends. The general Schrödinger equation tells you that time evolution of a quantum state is described by the Hamiltonian. The non-relativistic Hamiltonian gives you then the non-relativistic approximation of whatever field you're considering (spin 1/2, spin 0, ...)

 

[malawi_glenn]

@haushofer problem with that is that you are then describing a classical (non-quantum) field.

I can think of the The Schwinger-Dyson equations which in some sense gives the quantum equations of motion.

 

[A. Neumaier]

What is the Schrödinger equation in QFT? is it the nonrelativistic approximation of a Klein-Gordon scalar field?

No.

The Schrödinger equation $i\hbar \dot\psi=H\psi$ holds in relativistic quantum field theory for every state $\psi$, with $H$ being the generator of time translations of the Poincare group.

I have read that the Schrödinger equation describes a QFT in 0 dimensions.

A QFT in 0 space dimensions decribes (in the simplest case) an anharmonic oscillator in the Heisenberg picture, whereas the Schrödinger equation decribes (in the simplest case) an anharmonic oscillator in the Schrödinger picture. Both descriptions are equivalent, but the Schrödinger picture is usually easier to handle, hence is the way most commonly taught.

A nonrelativistic field theory in 3 space dimensions is the second quantized form of the multiparticle Schrödinger equation with an indefinite number of particles.

 

[accdd]

where?

That sentence is wrong, sorry, I meant to say I read online (a question on stackexchange) that quantum mechanics is related to scalar QFT in 0+1 dimensions. I would like to know more about it.

 

[malawi_glenn]

I would like to know more about it.

Try this https://authors.library.caltech.edu/8383/1/BOOejp07b.pdf

 

[accdd]

Thanks to everyone

 

[A. Neumaier]

Thanks to everyone

You might also be interested in reading the section 'Why does QFT look so different from QM?' in Chapter B8 of my Theoretical Physics FAQ.