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Gokul43201

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You will find the derivation in any Stat Mech textbook (such as Reif, Pathria, or Hwang)Ruslan_Sharipov said:Is there a proof for Fermi and Bose statistics? What is the background of this proof?

What does this question mean ? Are you asking if there are approximations used or do you mean something else?To what extent it is mathematically strict?

No other quantum statistics of indistinguishable particles can exist. Since the probability density should be invariant under interchange of indistinguishable particles, the wavefunction can only be one of two things :Can one prove that no other statistics is posible?

(i) symmetric, or (ii) anti-symmetric. Those are the only possibilities. The first leads to BE statistics and the second, to FD statistics.

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I am not sure it's that simple. I am not in a position to discuss parastatistics or parasupersymmetry (I just don't know any details). But there are composite particles. Is deuton a boson? Not quite (see, e.g., H.J.Lipkin, Quantum Mechanics (North-Holland/American Elsevier, 1973 (to R.S.: there is a Russian translation)).Gokul43201 said:No other quantum statistics of indistinguishable particles can exist. Since the probability density should be invariant under interchange of indistinguishable particles, the wavefunction can only be one of two things :

(i) symmetric, or (ii) anti-symmetric. Those are the only possibilities. The first leads to BE statistics and the second, to FD statistics.

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Physics Monkey

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This is what I know about it, I would be happy to hear from someone more informed if I have it wrong.

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Gokul43201

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So, it really comes down to how you want to do the math - even a seemingly strongly interacting system can be cleverly magicked into a weakly interacting system by renormalizing the correlations into say, an effective mass/charge. Having done that, you can use the simpler statistics of the quasiparticles to deal with the behavior of the system.

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Hi, just to provide a reference. Like Gokul43201 indirectly suggests, statistics is a symmetry (under the permutation group) of the wave function under *idealized* interaction assumptions. In the same way is the kinematical decoupling of the internal degrees of freedom from external ones just that : a simplifying assumption (which is quite dangerous in some circumstances in my mind). So, using statistics is a matter of good judgement; however it is not a *fundamental* principle in my mind (while flat space particle physicists promote it as such), just a very good effective way of understanding more complicated things. A good reference for starters (albeit a bit mathematical) in that respect is : ``particle statistics in three dimensions´´ Phys Rev. D. Vol 27, number 3, 1787...1797. Sorkin has developped the statistics of topological three geons in the context of canonical quantum gravity.Physics Monkey said:In three or more dimensions, Bose and Fermi statistics are the only possibilities. .

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Well, Fermi-Dirac and Bose-Einstein statistics combined with the special theory of relativity lead in a natural way to the Pauli-Lüders theorem of spin & statistics. Violations of this theorem, beside the ones already stated, appear in the quantum field theory of gauge systems where one introduces (anti)ghost fields (in the Hamiltonian BRST quantization) or antifields and ghosts in the Batalin-Vilkovisky (or the antifield-antibracket) formalism...Ruslan_Sharipov said:

Daniel.

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I guess the intuitive understanding of this is that prensence of gauge fieds make the particles (slightly) distinguishable ?dextercioby said:Well, Fermi-Dirac and Bose-Einstein statistics combined with the special theory of relativity lead in a natural way to the Pauli-Lüders theorem of spin & statistics. Violations of this theorem, beside the ones already stated, appear in the quantum field theory of gauge systems where one introduces (anti)ghost fields (in the Hamiltonian BRST quantization) or antifields and ghosts in the Batalin-Vilkovisky (or the antifield-antibracket) formalism...

Daniel.

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Daniel.

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So could you illuminate then what precisely goes wrong (I knew of what you said regarding field theory and gauge fixing procedures, but there should be a better way to understand this) ? You seem to say for example that the commutation relations for two integer spin field operators at spacelike separated events do not hold anymore. So what identity between them does hold such that causality is not violated ??dextercioby said:

Daniel.

I was more hinting at the fact that you can derive the possible *statistics* for N particles without using quantum field theory at all, but that you need to assume that particles are perfectly indistinguishable or distinguishable (that is what Sorkin does in this paper). Now, for a relativist these are very fishy concepts ... and much has been written on this issue (unfortunatly QFT theorists have a rather one sided view on this matter).

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I agree. I'd like just to emphasize that there are extremely important exceptions (not just some exotic systems), such as BCS theory of superconductifity, where Cooper pairs may be considered as composite particles, and their density is high, so Fermi or Bose statistics is not appropriate (see the above-quoted Lipkin's book).Gokul43201 said:

So, it really comes down to how you want to do the math - even a seemingly strongly interacting system can be cleverly magicked into a weakly interacting system by renormalizing the correlations into say, an effective mass/charge. Having done that, you can use the simpler statistics of the quasiparticles to deal with the behavior of the system.

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:rofl: hmm, many people will disagreedextercioby said:Nope, gauge symmetry is bad for physics,

Are you saying this happens all the time ? I mean in every interaction and at every energy scale ? I hope not, because it is wrong.it yields an infinite path integral, because the number of degrees of freedom is less than the number implied in the functional integration.

Nope, you can fix any gauge without using ghost fields and such fields are also used outside gauge fixing.Technically, ghost fields are used in "gauge fixing".

Ofcourse, the Fadeev Poppov ghost fields are used to get rid of the unphysical degrees of freedom that arise due to gauge fixing.

marlon

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Yes, our hungarian collegue does not seem to have learned that gauge symmetries improve renormalizabilty of the corresponding QFT. As a small remark: the other gauge fixing procedure you are referring to can be technically rather problematic, no?marlon said::rofl: hmm, many people will disagree

Are you saying this happens all the time ? I mean in every interaction and at every energy scale ? I hope not, because it is wrong.

Nope, you can fix any gauge without using ghost fields and such fields are also used outside gauge fixing.

Ofcourse, the Fadeev Poppov ghost fields are used to get rid of the unphysical degrees of freedom that arise due to gauge fixing.

marlon

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Certainly. That fact that Fadeev-Popov ghosts "exist" should say enoughCareful said:As a small remark: the other gauge fixing procedure you are referring to can be technically rather problematic, no?

marlon

edit : isn't Dexter Romanian ?

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Well, I must have made that mistake by observing this creature from outer spacemarlon said:edit : isn't Dexter Romanian ?

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