How does QFT handle particle creation and conversion?

[ftr]

I was reading this thread by stevendaryl
https://www.physicsforums.com/threads/second-quantization-vs-many-particle-qm.835472/

I have two questions

1. which QFT picture are those, Schrödinger, path integral or Heisenberg.

2.In QM the creation/annihilation operators raise and lower energies, but they don't create and destroy particles in the strict sense, let alone the particles having different spins, being scalar one time and bispinor another and vector in another. So why it is said that QFT is a generalization of multi particle QM, and how does QFT generate those different particle and converts them one type to another or others.

 

[stevendaryl]

I was reading this thread by stevendaryl
https://www.physicsforums.com/threads/second-quantization-vs-many-particle-qm.835472/

I have two questions

1. which QFT picture are those, Schrödinger, path integral or Heisenberg.

2.In QM the creation/annihilation operators raise and lower energies, but they don't create and destroy particles in the strict sense, let alone the particles having different spins, being scalar one time and bispinor another and vector in another. So why it is said that QFT is a generalization of multi particle QM, and how does QFT generate those different particle and converts them one type to another or others.

As to question number 2, I'm not talking about the raising and lowering operators for the simple harmonic oscillator. I'm talking about a mathematical operation that takes you from a space of $n$ particles to a space of $n+1$ particles. In nonrelativistic quantum mechanics, this operator doesn't correspond to anything physical, but it can be used to formulate many-particle theories in a way that is equivalent to the usual theories.

 

[ftr]

Thanks for the answer. what about the first question. it looks like the second method is Heisenberg picture , is that correct. what about the first one and in which qft application is used QED or QCD or scattering ...what. Thanks

 

[stevendaryl]

Thanks for the answer. what about the first question. it looks like the second method is Heisenberg picture , is that correct. what about the first one and in which qft application is used QED or QCD or scattering ...what. Thanks

The approach I described starts with single-particle QM in the Schrödinger representation and develops multi-particle QM in the Heisenberg representation. The big difference is whether you have a differential equation for the wave function or for the field operators.