Relationships between QM and QFT Particles

[DrDu]

I don't think this is mainly a question of mathematical rigor. The Wightman axioms are very physical.
If a reasonable physical QFT would exist, we should be able to write down its Hamiltonian.

 

[Buzz Bloom]

Hi DrDu and atyy:

Thank you both for your most recent posts. Just when I thought I had established for myself a satisfactory understanding of the relationships betweeen QM and QFT for my mental capacity to grasp, you have added some more concepts. I now feel prompted to ask additional questions.

I gather that QFTs have a close connection with particle physics, includng the Lie groups used to express field/particle properties. I get the impression that QM, specifically with its limitation rearding particle number conservation, doesn't have much or anything to do with particle physics. Is this correct?

The question is open in 3+1D

From this quote, atyy, I guess that QM applies OK to a 3D-space, 1D-time spacetime (as well as spacetimes with 1D and 2D spaces) , while currently QFTs fail on problems involving spacetime with 3D space. Is this correct?

Regards,
Buzz

 

[atyy]

I don't think this is mainly a question of mathematical rigor. The Wightman axioms are very physical.
If a reasonable physical QFT would exist, we should be able to write down its Hamiltonian.

What I meant was that there are QFTs in 2+1D that fulfill the Wightman axioms. From the informal point of view, physicists would understand these QFTs using a Fock space which is a "particle space", but from the rigourous point of view, the Hilbert space of these QFTs is not a Fock space in the physicists' sense.

 

[naima]

but from the rigourous point of view, the Hilbert space of these QFTs is not a Fock space in the physicists' sense.

What is missing for a rigorous Fock space in the cited models?