A Quantum Field theory vs. many-body Quantum Mechanics

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The discussion centers on the equivalence of Quantum Field Theory (QFT) and many-body Quantum Mechanics (QM), with participants highlighting key differences. Critics argue that QFT can address phenomena such as instantons and topological effects that many-body QM struggles with, particularly in complex manifolds. The conversation also touches on the treatment of quasiparticle excitations, with some suggesting that many-body QM cannot adequately describe certain condensed matter systems like strange metals. While some participants assert that many-body QM is a subset of QFT, others emphasize the limitations of many-body QM in handling arbitrary topologies. Overall, the debate underscores the nuanced relationship between these two frameworks in quantum physics.
  • #31
I remember I've read a paper, stating qft inherits traits of the particle formalism. In the sense qft formulation is not superior, than the many-body qm.
 
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  • #32
QFT formulation is superior in all cases, where you have particle creation and destruction processes and equivalent to (many-body) QM if this is not the case.
 
  • #33
vanhees71 said:
QFT formulation is superior in all cases, where you have particle creation and destruction processes and equivalent to (many-body) QM if this is not the case.
I agree, this is what it seems. Nevertheless this is what I've read. I'm actually curious if qft can be the result of the missing information. There is a certain analogy with the ordinary information transfer. Quantum fields look like a superposition of causal sets.
 
  • #34
Fractal matter said:
I agree, this is what it seems. Nevertheless this is what I've read. I'm actually curious if qft can be the result of the missing information. There is a certain analogy with the ordinary information transfer. Quantum fields look like a superposition of causal sets.
Can you give more details on this or provide a reference?
 
  • #35
Joker93 said:
Can you give more details on this or provide a reference?
What exactly are you interested in ? I don't remember the title of the 1st paper. As for the missing information there are quite a few. For example: Quantum States as Ordinary Information - https://www.mdpi.com/2078-2489/5/1/190 I don't know the details, just in general.
 
  • #36
Demystifier said:
Some effects may be described by topological effective field theory, in which case it may not have quasiparticle excitations.
Can you give an example please ? I'm interested in all the cases in which the effective theory doesn't have quasiparticles.
 
  • #37
Fractal matter said:
Can you give an example please ? I'm interested in all the cases in which the effective theory doesn't have quasiparticles.
All topological field theories lack propagating degrees of freedom and hence (quasi)particles. An example of topological field theory is Chern-Simons theory. In condensed matter, it plays a role in a description of quantum Hall effect (see e.g. https://arxiv.org/abs/1606.06687). Roughly speaking, in the quantum Hall effect the EM field interacts with matter in such a way that the effective dressed EM field cannot propagate through the material, so the dressed EM field does not have dressed photon excitations.
 
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