Quantum Field theory vs. many-body Quantum Mechanics

[Joker93]

TL;DR Summary

Many people say that the two are equivalent. Is this true?

A lot of people say that Quantum Field theory (QFT) an Quantum Mechanics (QM) are equivalent. Yet, I've found others who dispute these claims. Among the counter-arguments (which I admittedly do not have the expertise to pick apart and check their validity in full) are the following:
1) While QFT can fully capture instantonic solutions, many-body QM cannot. I've seen instantons in the context of QM though.
2) While QFT can fully capture topological phenomena, many-body QM cannot. I know that QM can capture at least some topological phenomena, such as the integer quantum hall effect (although I do not know if the description of edge states is present in the context of QM, whereas in the context of QFT they are decribed by Chern-Simons theories).
3) I do not know if there is a many-body QM correspondence to topological field theories.
4) There are QFT systems in condensed matter physics which do not admit quasiparticle excitations, such as the strange metal phase in superconductors. I do not think (but I'm not sure) if such systems can be described by many-body QM.
5) Say we have a scalar field in QFT, which lives on a manifold, M. Then a scalar field is a function M->R. I know that when M is Euclidean with trivial topology, we're talking about Galilean QM which has a formulation in both QFT and many-body QM. If M is Minkowski, then I know QFT is the better framework to work in, although I do not know if you can also work in this space with many-body QM. Yet, if the manifol M is generally a curved, complex manifold with non-trivial topology, while QFT can handle it, I highly doubt that many-body QM can describe it.
6) Some say that the two are equivalent only in the case where the particle number in many-body QM is conserved. In elementary systems that I've studied, this turns out to be true. Alas, I do not know if it's true in general (i.e. when the particle number is not conserved).

On the other hand, I know that one-body QM can be rigorously considered as being a (0+1)-diimensional QFT (with fields being the particle's position, themselves only depending on time), I do not know if and how I would make such an analogy between many-body QM with a (some+some)-dimensional QFT. If such a mapping doesn't exist, then this would - in my humble, naive and maybe ignorant opinion - be a conclusive argument as to the two not being equivalent.

By not necessarily basing your arguments just on the points given above, what is your take on it?

 

[PeterDonis]

A lot of people say

Who? Please give specific references.

I've found others who dispute these claims.

Who? Please give specific references.

 

[Joker93]

Who? Please give specific references.Who? Please give specific references.

Weinberg, vol1 of his QFT books implies that the two approaches lead to the same results. McGreevy also has notes on his website for his QFT-related courses in which he states what I said in my final paragraph. My point (4) is mentioned in the first pages of the book "Holographic quantum matter" by Hartnoll et al. Point (6) I've found it in many books and websites over the years but I cannot remember where exactly off the top of my head. Same goes for (1) and (2). Points (3) and (5) are my speculations.

All in all, I do not think that who said what is relevant here. I might be wrong on all accounts. I just asked people's opinions on this. While I haven't been able to find extended discussion on this here, I did find the following relevant links which give information about the various points I mentioned above. They are the following:
https://physics.stackexchange.com/q...-body-theory-and-quantum-field-theory-methods

https://physics.stackexchange.com/questions/54854/equivalence-between-qft-and-many-particle-qm

https://physics.stackexchange.com/q...onical-quantization-of-fields-and/87194#87194

https://physics.stackexchange.com/q...ield-theory-equivalent-with-quantum-mechanics

Thanks.

 

[PeterDonis]

All in all, I do not think that who said what is relevant here.

Yes, it is, for two reasons. First, specific references to specific statements by specific authors are always a better basis for discussion than vague generalizations about what "people" say. Multiple specific references are fine; then we can compare and contrast what different authors say and offer our own opinions and comments.

Second, it's much better to reference directly what other people say than to try to paraphrase it in your own words. This is particularly true in technical discussions where fine details of the exact words and terms people used can make a big difference.

 

[Demystifier]

Summary:: Many people say that the two are equivalent. Is this true?

By not necessarily basing your arguments just on the points given above, what is your take on it?

The confusion arises from the fact that nonrelativistic QFT in condensed matter physics deals with two kinds of particles. One kind are the fundamental particles, typically electrons. Those particles are treated nonrelativistically so their number is fixed. Nonrelativistic QFT, called also second quantizaton in this context, is just a mathematical trick to make sure that the many-body wave function of electrons is antisymmetric. So it's equivalent to nonrelativistic QM combined with appropriate antisymmetrization.

The other kind of particles are quasiparticles, the best known example of which are phonons. Those can be created and destructed. In the long wavelength limit, they can even satisfy a Lorentz invariant dispersion relation (with the speed of sound instead of the speed of light). Quasiparticle excitations can be described by effective field theory, which is not the same thing as the fundamental field theory of electrons that we started with. Some effects may be described by topological effective field theory, in which case it may not have quasiparticle excitations. But in principle, all this can be derived from the "fundamental" nonrelativistic theory of electrons that we started with, either in the first or second quantized form.

So to make the long story short, the nonrelativistic field theory of electrons is equivalent to many-body QM of electrons, but effective condensed matter field theory is not equivalent to many-body QM of quasiparticles.

 

[Joker93]

Yes, it is, for two reasons. First, specific references to specific statements by specific authors are always a better basis for discussion than vague generalizations about what "people" say. Multiple specific references are fine; then we can compare and contrast what different authors say and offer our own opinions and comments.

Second, it's much better to reference directly what other people say than to try to paraphrase it in your own words. This is particularly true in technical discussions where fine details of the exact words and terms people used can make a big difference.

This is true. I ultimately agree. My initial problem was that a lot of what I said were things that are commonly found in books so I thought (maybe wrongly) that references wouldn't be needed. The rest was my speculation, which I believe I wrote them in a way to reflect that.
In any case, I hope this helps clarify some things :)
Thanks for the feedback.

 

[Joker93]

The confusion arises from the fact that nonrelativistic QFT in condensed matter physics deals with two kinds of particles. One kind are the fundamental particles, typically electrons. Those particles are treated nonrelativistically so their number is fixed. Nonrelativistic QFT, called also second quantizaton in this context, is just a mathematical trick to make sure that the many-body wave function of electrons is antisymmetric. So it's equivalent to nonrelativistic QM combined with appropriate antisymmetrization.

The other kind of particles are quasiparticles, the best known example of which are phonons. Those can be created and destructed. In the long wavelength limit, they can even satisfy a Lorentz invariant dispersion relation (with the speed of sound instead of the speed of light). Quasiparticle excitations can be described by effective field theory, which is not the same thing as the fundamental field theory of electrons that we started with. Some effects may be described by topological effective field theory, in which case it may not have quasiparticle excitations. But in principle, all this can be derived from the "fundamental" nonrelativistic theory of electrons that we started with, either in the first or second quantized form.

So to make the long story short, the nonrelativistic field theory of electrons is equivalent to many-body QM of electrons, but effective condensed matter field theory is not equivalent to many-body QM of quasiparticles.

So, essentially, if I understood correctly, the many-body QM (which includes the second quantization and the effective field theories that you mentioned) is a subset of QFT? Based on your answer, I can't see how many-body QM can properly treat particles/fields existing in a generic manifold of an arbitrary topology. Is this assessment correct?

A sub-question: the Lorentz invariant dispersion relation that you mentioned, is that near the Dirac or Weyl cones?

 

[Demystifier]

So, essentially, if I understood correctly, the many-body QM (which includes the second quantization and the effective field theories that you mentioned) is a subset of QFT?

Yes.

Based on your answer, I can't see how many-body QM can properly treat particles/fields existing in a generic manifold of an arbitrary topology.

What do you mean by "arbitrary"? If it's topology that appears in condensed matter physics, than many body QM of electrons and atoms can treat it. If it's topology that appears in gravity and cosmology, then many body QM of electrons and atoms cannot treat it.

A sub-question: the Lorentz invariant dispersion relation that you mentioned, is that near the Dirac or Weyl cones?

Remind me what's the difference!

 

[Joker93]

What do you mean by "arbitrary"? If it's topology that appears in condensed matter physics, than many body QM of electrons and atoms can treat it. If it's topology that appears in gravity and cosmology, then many body QM of electrons and atoms cannot treat it.

I'm talking about both QFT and many-body QM as general frameworks rather than models. You can construct a QFT no matter what the underlying manifold is. On the other hand, while many-body QM is used for some manifolds with non-trivial topologies (such as when you impose periodic boundary conditions in configuration space), I don't see how it can generalize to other non-trivial manifolds. All I'm saying is that I can't see how many-body QM can even treat every condensed matter system; I know that there are systems, even in condensed matter (such as the strange metals I mentioned in my question) that do not admit quasiparticle excitations. For those systems, a QFT approach seems to be the only viable one.

Remind me what's the difference!

Weyl cones have additional symmetry properties that only allow them to come in pairs. The Weyl cones correspond to Weyl fermions which follow the dispersion relation around the Weyl point. An analogous thing goes for Dirac cones. Both dispersion relations seem to respect Lorentz invariance if I remember correctly.

 

[Demystifier]

All I'm saying is that I can't see how many-body QM can even treat every condensed matter system; I know that there are systems, even in condensed matter (such as the strange metals I mentioned in my question) that do not admit quasiparticle excitations. For those systems, a QFT approach seems to be the only viable one.

I don't believe that there is a condensed matter system that cannot be described by many-body QM in principle. But in some cases it's too complicated in practice (many-body problems are often very hard), so in practice people only know how to do it with effective field theory.

An example is fractional Hall effect, which is usually treated with effective field theory, but there is also a known way to treat it with many-body QM (Laughlin wave function).

 

[Joker93]

I don't believe that there is a condensed matter system that cannot be described by many-body QM in principle. But in some cases it's too complicated in practice (many-body problems are often very hard), so in practice people only know how to do it with effective field theory.

An example is fractional Hall effect, which is usually treated with effective field theory, but there is also a known way to treat it with many-body QM (Laughlin wave function).

I see. But what about cases where we know for a fact that there are no quasiparticle excitations? Doesn't that mean that a "particle approach" is invalid in those cases?

 

[Demystifier]

I see. But what about cases where we know for a fact that there are no quasiparticle excitations? Doesn't that mean that a "particle approach" is invalid in those cases?

No. There are no quasiparticles, but there are particles (electrons).

 

[Joker93]

No. There are no quasiparticles, but there are particles (electrons).

So, in principle you can employ a second quantization approach in which you inlcude the fundamental particles involved in the interactions of a such a condensed matter system, but in practice this is intractable and this is why researchers use different methods in such cases?

If so, it indeed doesn't invalidate the use of second quantization. But it brings us then to the question of why is many-body QM considered -as you mentioned- as a subset of QFT. Is it becayse it can do anything that QFT does in a Galilean context? In vol.1 of Weinberg's QFT books, he does show that even in a Lorentzian context, the two are still equivalent, in that you can start building your many-body QM approach from products of single-particle states.

Oh, I think I'm confused :D

 

[vanhees71]

Summary:: Many people say that the two are equivalent. Is this true?

A lot of people say that Quantum Field theory (QFT) an Quantum Mechanics (QM) are equivalent. Yet, I've found others who dispute these claims.

It's a bit a question of defining your terms. For me "Quantum Mechanics" (QM) is non-relativistic quantum mechanics of a fixed number of (distinguishable or indistinguishable) particles. This theory can be described in the "first-quantization formalism", working with a wave function of the type $\psi(\xi_1,\xi_2,\ldots,\xi_N)$, where $\xi_k$ denote eigenvalues of a complete set of single-particle observables, usually $(\xi_k)=(\vec{x}_k,\sigma_k)$ with position vectors $\vec{x}_k$ and spin-$z$ components $\sigma_k$ for the k-th particle. It can be equivalently described by a quantum field theory. The only constraint is that the Hamiltonian must conserve the individual particles, i.e., there must not be annihilation and creation processes.

Quantum-field theory is however the most elegant way to precisely describe such "particle-changing" reactions. In this sense QFT is more general than QM, but contains QM as a special case.

Among the counter-arguments (which I admittedly do not have the expertise to pick apart and check their validity in full) are the following:
1) While QFT can fully capture instantonic solutions, many-body QM cannot. I've seen instantons in the context of QM though.

What are "instantonic solutions"? Indeed there are instantons in both QM and QFT, particularly related to tunneling phenomena of all kinds:

https://en.wikipedia.org/wiki/Instanton

2) While QFT can fully capture topological phenomena, many-body QM cannot. I know that QM can capture at least some topological phenomena, such as the integer quantum hall effect (although I do not know if the description of edge states is present in the context of QM, whereas in the context of QFT they are decribed by Chern-Simons theories).
3) I do not know if there is a many-body QM correspondence to topological field theories.
4) There are QFT systems in condensed matter physics which do not admit quasiparticle excitations, such as the strange metal phase in superconductors. I do not think (but I'm not sure) if such systems can be described by many-body QM.
5) Say we have a scalar field in QFT, which lives on a manifold, M. Then a scalar field is a function M->R. I know that when M is Euclidean with trivial topology, we're talking about Galilean QM which has a formulation in both QFT and many-body QM. If M is Minkowski, then I know QFT is the better framework to work in, although I do not know if you can also work in this space with many-body QM. Yet, if the manifol M is generally a curved, complex manifold with non-trivial topology, while QFT can handle it, I highly doubt that many-body QM can describe it.
6) Some say that the two are equivalent only in the case where the particle number in many-body QM is conserved. In elementary systems that I've studied, this turns out to be true. Alas, I do not know if it's true in general (i.e. when the particle number is not conserved).

On the other hand, I know that one-body QM can be rigorously considered as being a (0+1)-diimensional QFT (with fields being the particle's position, themselves only depending on time), I do not know if and how I would make such an analogy between many-body QM with a (some+some)-dimensional QFT. If such a mapping doesn't exist, then this would - in my humble, naive and maybe ignorant opinion - be a conclusive argument as to the two not being equivalent.

By not necessarily basing your arguments just on the points given above, what is your take on it?

As I said, for sure many-body QM can be described using QFT. Quasiparticles like phonons, plasmons, etc. that can be destroyed or created and are thus best described using QFT. It doesn't matter whether you have a non-relativistic or a relativistic theory. QFT exists for both. In condensed-matter physics you usually have a non-relativistic theory. On the other hand there's also relativistic many-body theory, where you use relativistic many-body QFT (e.g., in my field of research, relativistic heavy-ion collisions, we also deal with quasiparticles to describe strongly interacting dense matter created in heavy-ion collisions).

 

[Joker93]

It's a bit a question of defining your terms. For me "Quantum Mechanics" (QM) is non-relativistic quantum mechanics of a fixed number of (distinguishable or indistinguishable) particles. This theory can be described in the "first-quantization formalism", working with a wave function of the type $\psi(\xi_1,\xi_2,\ldots,\xi_N)$, where $\xi_k$ denote eigenvalues of a complete set of single-particle observables, usually $(\xi_k)=(\vec{x}_k,\sigma_k)$ with position vectors $\vec{x}_k$ and spin-$z$ components $\sigma_k$ for the k-th particle. It can be equivalently described by a quantum field theory. The only constraint is that the Hamiltonian must conserve the individual particles, i.e., there must not be annihilation and creation processes.

Quantum-field theory is however the most elegant way to precisely describe such "particle-changing" reactions. In this sense QFT is more general than QM, but contains QM as a special case.

What are "instantonic solutions"? Indeed there are instantons in both QM and QFT, particularly related to tunneling phenomena of all kinds:

https://en.wikipedia.org/wiki/Instanton

As I said, for sure many-body QM can be described using QFT. Quasiparticles like phonons, plasmons, etc. that can be destroyed or created and are thus best described using QFT. It doesn't matter whether you have a non-relativistic or a relativistic theory. QFT exists for both. In condensed-matter physics you usually have a non-relativistic theory. On the other hand there's also relativistic many-body theory, where you use relativistic many-body QFT (e.g., in my field of research, relativistic heavy-ion collisions, we also deal with quasiparticles to describe strongly interacting dense matter created in heavy-ion collisions).

Understood.

So, can QM actually treat any underlying manifold space(time) with any topology, like QFT does? I've seen QM being able to be formulated for Euclidean (of course) and Lorentzian spacetimes, but what about general curved spacetimes with non-trivial topologies? QFT can handle it, but can many-body QM do that too?

 

[PeterDonis]

a lot of what I said were things that are commonly found in books so I thought (maybe wrongly) that references wouldn't be needed.

Wrongly. We still need a specific reference as a basis for discussion. What you gave in post #3 is fine.

The rest was my speculation

Please bear in mind that PF is not for discussing personal speculations. It looks like the thread discussion here has focused on non-speculative topics, which is fine.

 

[vanhees71]

Understood.

So, can QM actually treat any underlying manifold space(time) with any topology, like QFT does? I've seen QM being able to be formulated for Euclidean (of course) and Lorentzian spacetimes, but what about general curved spacetimes with non-trivial topologies? QFT can handle it, but can many-body QM do that too?

I don't know, but since the QFT formulation of many-body QM is already much more convenient than the 2nd-quantization formalism. For me it's much more easy to deal with bosonic or fermionic field operators than with symmetriced or antisymmetrized many-body wave functions.

For Lorentzian spacetime, i.e., special relativistic QT, the first-quantization formalism is very inconvenient. Although it's possible to start like Dirac in the first-quantization formalism and then reinterpret the troubles with "negative-frequency modes" by a many-body theory with non-conserved particles in terms of the filled Dirac sea, which leads to the hole-theoretical formulation of QED. I don't know, whether it's possible to also formulate non-Abelian gauge theories or the Standard Model in a hole-theoretical way, but it doesn't matter, because the QFT formulation is again much more convenient than the hole-theoretical formulation anyway.

I don't know, whether there's a QM formulation of QT in curved (background) space times at all.

 

[A. Neumaier]

can QM actually treat any underlying manifold space(time) with any topology, like QFT does? I

Yes. $N$-particle wave functions are functions $\psi(x_1,...,x_n)$ where the $x_k$ are points of a 3-dimensional manifold at a fixed time $t$ which may be varied as an additional argument of $\psi$.

I don't know, whether there's a QM formulation of QT in curved (background) space times at all.

Yes, there is. See the books by Wald or deWitt. The unsolved problems appear only when one wants to consider a back action of matter on the metric or even topology of the manifold.

 

[vanhees71]

Yes. $N$-particle wave functions are functions $\psi(x_1,...,x_n)$ where the $x_k$ are points of a 3-dimensional manifold at a fixed time $t$ which may be varied as an additional argument of $\psi$.

Yes, there is. See the books by Wald or deWitt. The unsolved problems appear only when one wants to consider a back action of matter on the metric or even topology of the manifold.

I know that there is QFT in curved spacetime, but QM? Of course there's still no Q(F)T of gravity/spacetime itself. In Wald's textbook there's of course QFT in curved spacetime, but I don't remember any section of QM in curved spacetime in this book.

 

[PeterDonis]

I don't know, whether there's a QM formulation of QT in curved (background) space times at all.

If by "QM" you mean non-relativistic QM, I'm not sure this would even make sense; non-relativistic QM doesn't use spacetime to begin with. In non-relativistic QM, gravity is modeled as a potential in the Hamiltonian.

 

[vanhees71]

True, but there might be attempts to formulate a QM in curved space time, which may have the chance to make sense, I'm not aware of. I doubt it since already in Minkowski space it is not really consistent. For fermionic QED you can reinterpret the relativistic Dirac equation minimally coupled to the em. field via hole theory. That's at the end equivalent to the QFT formulation, but nobody uses it anymore, because QFT is the much more natural formulation of QED and of coarse the entire standard model, which is a non-Abelian gauge theory, where I don't know, whether a hole-theoretical formulation is even possible.

 

[A. Neumaier]

I know that there is QFT in curved spacetime, but QM? Of course there's still no Q(F)T of gravity/spacetime itself. In Wald's textbook there's of course QFT in curved spacetime, but I don't remember any section of QM in curved spacetime in this book.

I was talking about nonrelativistic multiparticle quantum mechanics in curved space, with standard time. People interested in exactly solvable models discuss such things. I don't know of applications, though.

 

[samalkhaiat]

I was talking about nonrelativistic multiparticle quantum mechanics in curved space, with standard time. People interested in exactly solvable models discuss such things. I don't know of applications, though.

Setting up path integrals on multiply-connected spaces, for example, the path integral of a system whose external (position) coordinate moves in $\mathbf{R}^{3}$ and whose internal (spin) coordinate moves on $SO(3)$.

 

[Joker93]

I don't know, but since the QFT formulation of many-body QM is already much more convenient than the 2nd-quantization formalism. For me it's much more easy to deal with bosonic or fermionic field operators than with symmetriced or antisymmetrized many-body wave functions.

For Lorentzian spacetime, i.e., special relativistic QT, the first-quantization formalism is very inconvenient. Although it's possible to start like Dirac in the first-quantization formalism and then reinterpret the troubles with "negative-frequency modes" by a many-body theory with non-conserved particles in terms of the filled Dirac sea, which leads to the hole-theoretical formulation of QED. I don't know, whether it's possible to also formulate non-Abelian gauge theories or the Standard Model in a hole-theoretical way, but it doesn't matter, because the QFT formulation is again much more convenient than the hole-theoretical formulation anyway.

I don't know, whether there's a QM formulation of QT in curved (background) space times at all.

I always found QFT to be much more convenient when dealing with anything else than a flat Euclidean space (maybe with some non trivial topologies too, such as the ones arising in solid state physics where we impose periodic boundary conditions).
I guess, the question is more precisely put as "in principle, is QFT equivalent to many-body QM?".

 

[Joker93]

Yes. $N$-particle wave functions are functions $\psi(x_1,...,x_n)$ where the $x_k$ are points of a 3-dimensional manifold at a fixed time $t$ which may be varied as an additional argument of $\psi$.

Yes, there is. See the books by Wald or deWitt. The unsolved problems appear only when one wants to consider a back action of matter on the metric or even topology of the manifold.

Very interesting!
Can many-body QM also treat more complicated manifolds, such as complex ones (Kahler, Calabi-Yau) with arbitrary topologies (curled-up dimensions, holes, etc)?

 

[Joker93]

If by "QM" you mean non-relativistic QM, I'm not sure this would even make sense; non-relativistic QM doesn't use spacetime to begin with. In non-relativistic QM, gravity is modeled as a potential in the Hamiltonian.

I don't think the discussion here is focused on non-relativistic QM. The question is if the two approaches are equivalent in general, not in specific cases such as Euclidean spaces.

Setting up path integrals on multiply-connected spaces, for example, the path integral of a system whose external (position) coordinate moves in $\mathbf{R}^{3}$ and whose internal (spin) coordinate moves on $SO(3)$.

Yes, this does seem to work for general topologies. But, do you happen to know if the quantum mechanical path integral can handle generally curved, real or complex, Euclidean or Lorentzian (or anything else) manifolds of arbitrary topology and particle content (any spin)?
Because, in essence, we're trying to answer whether QFT and many-body QM (as frameworks) span the same "theory space", i.e. they can describe the same things (naturalness aside).

 

[A. Neumaier]

Can many-body QM also treat more complicated manifolds, such as complex ones (Kahler, Calabi-Yau) with arbitrary topologies (curled-up dimensions, holes, etc)?

There are no limitations, except that the number of particles must be fixed. Indeed, QM is precisely the restriction of QFT to an eigenspace of a number operator, hence works whenever the latter can be defined and commutes with the Hamiltonian.

The commutation requirement excludes interacting Lorentz invariant theories.

 

[Joker93]

There are no limitations, except that the number of particles must be fixed. Indeed, QM is precisely the restriction of QFT to an eigenspace of a number operator, hence works whenever the latter can be defined and commutes with the Hamiltonian.

The commutation requirement excludes interacting Lorentz invariant theories.

So, indeed, QFT is a more general framework which allows for particle number non-conservation.

 

[samalkhaiat]

Yes, this does seem to work for general topologies.

No, it does not. You need to path-integrate on simply-connected spaces. So, if $X$ is a space with a non-trivial fundamental group, i.e. $\pi_{1}(X) \neq \{e\}$, the propagator on $X$ is obtained by doing the path-integral on the (universal) covering space of $X$ which is simply-connected. In the spin example that I gave, we get the propagator on the space $\mathbb{R}^{3} \times \mbox{SO}(3)$ by doing the path-integral on the (simply-connected) universal covering space $\mathbb{R}^{3} \times \mbox{SU}(2)$.

do you happen to know if the quantum mechanical path integral can handle generally curved, ****, **** manifolds *****?

(The stars above stand for unnecessary words in your question). Depending on what you mean by “can handle” I would say that neither me nor anybody else know the answer. This is why we don’t have quantum gravity.

we're trying to answer whether QFT and many-body QM (as frameworks) ****** can describe the same things *****.

In the literatures, the phrase “many-particle QM” usually means n-particle (non-relativistic) QM with $[H,N] = 0$, i.e., the number of particles is a constant of motion. So, if you give me the Hamiltonian of your “many-particle QM”, I should be able to tell you whether or not there exists an equivalent non-relativistic QFT.

 

[vanhees71]

I always found QFT to be much more convenient when dealing with anything else than a flat Euclidean space (maybe with some non trivial topologies too, such as the ones arising in solid state physics where we impose periodic boundary conditions).
I guess, the question is more precisely put as "in principle, is QFT equivalent to many-body QM?".

Then the definite answer is "no", because QFT can deal with particle creation and annihilation processes, and QM (by definition) can't.

 

[Fractal matter]

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.

 

[vanhees71]

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.

 

[Fractal matter]

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.

 

[Joker93]

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?

 

[Fractal matter]

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.