What mediates the exchange force?

[Ben Wilson]

In many-body theory for electronic structure, fermions experience a force resulting from Pauli Exclusion. So by extension, would quarks and other subatomic fermions experience this force?

If so, what is the "high energy" physics side of the story to forces arising from exchange rules? Is it a fundamental force, or arising from fundamental forces?

 

[vanhees71]

In which sense do you think the Pauli exclusion principle leads to a force? Anyway, the notion of forces is a bit vague in context of QT. So I'd need a clear definition of what you mean by force here.

The Pauli exclusion principle just states that the N-body quantum states are totally antisymmetric under exchange of two identical fermions, not more nor less. What has this to do, in your view, with "forces"?

In high-energy physics we use relativistic QFT do describe quantum fields and their mutual interactions. You pretty quickly learn to think not in terms of forces anymore but in terms of the action principle (which becomes the more intuitive picture than the idea of forces also of classical physics as soon as you started to use it).

 

[Ben Wilson]

In which sense do you think the Pauli exclusion principle leads to a force? Anyway, the notion of forces is a bit vague in context of QT. So I'd need a clear definition of what you mean by force here.

The Pauli exclusion principle just states that the N-body quantum states are totally antisymmetric under exchange of two identical fermions, not more nor less. What has this to do, in your view, with "forces"?

In high-energy physics we use relativistic QFT do describe quantum fields and their mutual interactions. You pretty quickly learn to think not in terms of forces anymore but in terms of the action principle (which becomes the more intuitive picture than the idea of forces also of classical physics as soon as you started to use it).

as in the exchange force in electronic structure theory. I can tell your more of a specialist in high energy physics. In electronic structure calculations of atoms and molecules etc, electrons interact via not only from a coloumb force, but also an exchange force resulting from the PEP. I'm interested to see where this forces comes from at a deeper level.

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

 

[vanhees71]

Well, there are no forces, and Wikipedia sets "forces" in quotation marks. I still don't understand what's your question. The Wikipedia article is quite clear: There are additional terms in the matrix elements of the perturbation Hamiltonian from the fermionic nature of identical particles, which are termed the "exchange interaction". This is due to the fact that the wave functions for bosons (fermions) are necessarily totally symmetric (antisymmetric) under exchange of particles.

Of course, the "first-quantization" formulation in Wikipedia is pretty complicated compared to the field-theoretical treatment, leading to Feynman diagram rules (not only in relativistic QFT but also in non-relativistic many-body theory).

 

[PeterDonis]

The answer to the title question of this thread is "nothing"; as the Wikipedia article you linked to notes, the exchange interaction "is not a true force, as it lacks a force carrier". Trying to understand this interaction by analogy with interactions that are mediated by force carriers will lead you nowhere.

 

[Ben Wilson]

i think its unsatisfactory to say that it's just the result of an abstract mathmatical relation, there's definitely some connection related to the physics. Perhaps a spin-off question would be: why do fermions have Pauli exclusion? why must wave functions be anti-symmetric under exchange?

google says "In relativistic quantum field theory, the Pauli principle follows from applying a rotation operator in imaginary time to particles of half-integer spin." i don't understand that myself :(

 

[PeterDonis]

i think its unsatisfactory to say that it's just the result of an abstract mathmatical relation

Who is saying that?

why do fermions have Pauli exclusion?

Because that's the definition of a fermion.

why must wave functions be anti-symmetric under exchange?

Because that's how we observe actual particles like electrons and quarks to behave.

google says

That's not a sufficient reference. Please give a link to the exact place where your quote comes from (as far as I can tell it doesn't come from any of the Wikipedia pages you linked to).

 

[Ben Wilson]

Who is saying that?
Because that's the definition of a fermion.
Because that's how we observe actual particles like electrons and quarks to behave.
That's not a sufficient reference. Please give a link to the exact place where your quote comes from (as far as I can tell it doesn't come from any of the Wikipedia pages you linked to).

its not a reference I'm just asking if you understand that type of physics? don't take my wikipedia page as my argument i was just using it to let the other guy know wht i was on about. https://en.wikipedia.org/wiki/Pauli_exclusion_principle look under ... in advanced quantum theory.

 

[PeterDonis]

its not a reference I'm just asking if you understand that type of physics?

"The wave function is antisymmetric under particle exchange" is the understanding. That's the fundamental physics involved. Depending on what kind of specific model you are using, this fundamental physics can show up in various ways. None of them are usefully understood as a "force" mediated by an exchange particle.

 

[Ben Wilson]

"The wave function is antisymmetric under particle exchange" is the understanding. That's the fundamental physics involved. Depending on what kind of specific model you are using, this fundamental physics can show up in various ways. None of them are usefully understood as a "force" mediated by an exchange particle.

do you understand what this means? - "In relativistic quantum field theory, the Pauli principle follows from applying a rotation operator in imaginary time to particles of half-integer spin"

 

[PeterDonis]

do you understand what this means?

Not without context. Can you give a link to the source where you got this quote?

 

[Ben Wilson]

Not without context. Can you give a link to the source where you got this quote?

look at the post before

 

[leptonsoliton]

This topic keeps coming on this and other forums. I suppose it will continue to. The Pauli Exclusion Principle is a consequence of our current understanding of the rules of QM. It is not considered a force. There is no mediating exchange particle. This behavior of fermions is not a classical idea. To insist that it constitutes a force is to think classically. White dwarf and neutron stars behave the way they do because they obey the rules of QM. If the mass is too great, they collapse anyway. Does this mean that, at this point, QM has broken down (due to not taking gravity into account)? Or does the complexity of the problem permit enough allowable states? Perhaps gravity allows extra states. Perhaps PEP looks different with gravity in it.

 

[Ben Wilson]

This topic keeps coming on this and other forums. I suppose it will continue to. The Pauli Exclusion Principle is a consequence of our current understanding of the rules of QM. It is not considered a force. There is no mediating exchange particle. This behavior of fermions is not a classical idea. To insist that it constitutes a force is to think classically. White dwarf and neutron stars behave the way they do because they obey the rules of QM. If the mass is too great, they collapse anyway. Does this mean that, at this point, QM has broken down (due to not taking gravity into account)? Or does the complexity of the problem permit enough allowable states? Perhaps gravity allows extra states. Perhaps PEP looks different with gravity in it.

I don't mean to impose classical thinking by loosely using the word force, I'm tentatively referring to, e.g., the "balance" against electro-nuclear coloumb attraction. With a question like this, we need to be careful not to be lazy, it's laziness in answering this question that keeps bringing it back up.

It's interesting that you bring up gravity, maybe PEP is an incomplete rule and the answer lies in quantum gravity? or maybe the answer to quantum gravity lies in applying a bit more scrutiny to the PEP? That's why I'm interested to know how PEP has developed in nature, to say that it just "is" is not good enough for a physicist.

 

[PeterDonis]

If the mass is too great, they collapse anyway. Does this mean that, at this point, QM has broken down (due to not taking gravity into account)?

No, it just means that the ability of fermions to resist compression is finite, and sufficiently intense gravity can overcome it.

 

[PeterDonis]

maybe PEP is an incomplete rule and the answer lies in quantum gravity?

Please review the PF rules on personal speculations. There is no need to invoke quantum gravity to explain why sufficiently massive white dwarfs or neutron stars are unstable; the standard models of these objects using GR and QM work just fine.

That's why I'm interested to know how PEP has developed in nature

I don't understand what you mean. The PEP is a property of all fermions; it doesn't "develop", it just is.

What textbooks or peer-reviewed papers on QM and the PEP have you read? If your understanding comes entirely from Wikipedia, it's not going to be very good.

 

[Ben Wilson]

No, it just means that the ability of fermions to resist compression is finite, and sufficiently intense gravity can overcome it.

i'm afraid you are wrong, the popular consensus is QM is broken in this scenario

 

[PeterDonis]

For more detailed information on the maximum mass limits for white dwarfs and neutron stars and how they are modeled, see the references given in these Wikipedia articles:

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

https://en.wikipedia.org/wiki/Tolman–Oppenheimer–Volkoff_limit

 

[Ben Wilson]

For more detailed information on the maximum mass limits for white dwarfs and neutron stars and how they are modeled, see the references given in these Wikipedia articles:

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

https://en.wikipedia.org/wiki/Tolman–Oppenheimer–Volkoff_limit

I'm proud to have graduated from the university of wikipedia magnum cum laude thank you very much. I'm sure you know what is meant by "In relativistic quantum field theory, the Pauli principle follows from applying a rotation operator in imaginary time to particles of half-integer spin."? is it really necessary to find the page in a spin stats textbook that explains this before you'll explain it in 20 seconds? cus then i may as well give up my tenure at wikipedia entirely

 

[Jomenvisst]

I suspect the confusion arises when thinking of a many electron system, that is properly described only by a many body wavefunction, in terms of single electrons interacting, in some sense, as classical particles. I think a helpful concept if you still want to pursue that line is that of the "exchange-correlation hole" as developed in density functional theory, see for instance : http://cmt.dur.ac.uk/sjc/thesis_ppr/node28.html .

 

[PeterDonis]

i'm sure you know what is meant by "In relativistic quantum field theory, the Pauli principle follows from applying a rotation operator in imaginary time to particles of half-integer spin."?

Not without context. See below.

is it really necessary to find the page in a spin stats textbook that explains this

If you want to be taken seriously, yes, you need to find a mainstream source and reference it. Otherwise I have no idea whether you actually got this from a spin stats textbook, whether it came from some pop science article that might be distorting or misdescribing the physics, or whether you just made it up yourself. We have rules about acceptable sources here at PF for a reason. If you actually did get this from a mainstream source, it would have taken less effort for you to just reference it than you have already expended in failing to reference it.

cus then i may as well give up my tenure at wikipedia entirely

That might be a good idea if you actually want to understand physics.

 

[Ben Wilson]

I suspect the confusion arises when thinking of a many electron system, that is properly described only by a many body wavefunction, in terms of single electrons interacting, in some sense, as classical particles. I think a helpful concept if you still want to pursue that line is that of the "exchange-correlation hole" as developed in density functional theory, see for instance : http://cmt.dur.ac.uk/sjc/thesis_ppr/node28.html .

you're right i am confused. in dft what i understand as the exchange corellation arises from single particle exchange corellation functionals using locally isotropic or gradient approximations of a mean particle density. I'm not sure moving away from spin orbitals to kohn-sham orbitals helps me in my reasoning.

 

[Ben Wilson]

Not without context. See below.
If you want to be taken seriously, yes, you need to find a mainstream source and reference it. Otherwise I have no idea whether you actually got this from a spin stats textbook, whether it came from some pop science article that might be distorting or misdescribing the physics, or whether you just made it up yourself. We have rules about acceptable sources here at PF for a reason. If you actually did get this from a mainstream source, it would have taken less effort for you to just reference it than you have already expended in failing to reference it.
That might be a good idea if you actually want to understand physics.

i have lol i told u in the first place https://en.wikipedia.org/wiki/Pauli_exclusion_principle

 

[PeterDonis]

i have lol i told u in the first place

That's not a valid reference. Read the PF rules.

Thread closed. If you have a valid reference, you can PM me.