A Schrodinger equation in quantum field theory

accdd
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What is the Schrodinger equation in QFT? is it the nonrelativistic approximation of a Klein-Gordon scalar field? or Is there more?
I have read that the Schrodinger equation describes a QFT in 0 dimensions.
I accept every answer
 
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accdd said:
I have read that the Schrodinger equation describes a QFT in 0 dimensions.
where?
 
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accdd said:
What is the Schrodinger equation in QFT? is it the nonrelativistic approximation of a Klein-Gordon scalar field? or Is there more?
I have read that the Schrodinger equation describes a QFT in 0 dimensions.
I accept every answer
It depends. The general Schrodinger 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, ...)
 
@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.
 
accdd said:
What is the Schrodinger 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.

accdd said:
I have read that the Schrodinger 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.
 
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malawi_glenn said:
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.
 
Thanks to everyone
 

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