Pauli's Exclusion Principle

[Alan Grayson]

Does the Pauli's Exclusion Principle have a similar status in QM as Born's rule; namely, an empirical fact not derivable from the postulates of QM? TIA, AG

[John Clark]

On Thu, Apr 2, 2020 at 9:09 PM Alan Grayson <agrays...@gmail.com> wrote:

> Does the Pauli's Exclusion Principle have a similar status in QM as Born's rule; namely, an empirical fact not derivable from the postulates of QM? TIA, AG

Yes.

John K Clark

[Lawrence Crowell]

It is reasonable to state the Pauli exclusion principle is a postulate on its own. There are though other possibilities. With supersymmetry, parafermions, bosonization and now fermionization of bosons the role of the PEP is not entirely certain. 

LC

[Brent Meeker]

But it's derivable from QM + special relativity, c.f. https://en.wikipedia.org/wiki/Spin%E2%80%93statistics_theorem

Brent

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[Russell Standish]

I thought the principle came from antisymmetry of fermionic pairwise
wavefunctions. If two fermions occupied the same state, then
antisymmetry is impossible. Bosons have symmetric pairwise
wavefunctions (you can swap two bosons, and nothing changes), hence it
is possible to have more than one boson in the same state.

I'd have to go back to my class notes of QM to check this of course,
just speaking from 35+ years ago when I last studied this.

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[Bruce Kellett]

On Sat, Apr 4, 2020 at 7:36 PM Russell Standish <li...@hpcoders.com.au> wrote:

I thought the principle came from antisymmetry of fermionic pairwise
wavefunctions. If two fermions occupied the same state, then
antisymmetry is impossible. Bosons have symmetric pairwise
wavefunctions (you can swap two bosons, and nothing changes), hence it
is possible to have more than one boson in the same state.

As I recall it, this is completely right. I think it all goes back to the nature of the 4-component spinors of Dirac theory -- rotation by 360 degrees changes the sign, necessitating the antisymmetric nature of the quantum state. Fermi-Dirac statistics, and as has been said, the fundamental spin-statistics theorem.

Bruce 

[Lawrence Crowell]

That is basically the case. The fermionic wave function is ψ is such that under the parity operator Pψ = -ψ. The standard example is the sin function. 

This gets more subtle with bosonization with χ = ψexp(εψ), where with ε^2 = 0 then  χ = ψ + εψψ so there is a fermionic plus the square of fermions = bosonic part. For ε a Grassmann number this is a form of supersymmetry. The Thirring fermion theory with a quartic V = ψ^†ψψ^†ψ potential leads to a bosonization of fields φ with a sin(φ) terms that gives the sine-Gordon equation. This describes the Josephson junction theory of superconductivity.  There are further developments with parafermions and so forth, and evcn how bosons can in restricted dimension give fermions. There is waiting in the wings I think a general physics of fermions and bosons.

LC

On Saturday, April 4, 2020 at 3:36:17 AM UTC-5, Russell Standish wrote:

I thought the principle came from antisymmetry of fermionic pairwise
wavefunctions. If two fermions occupied the same state, then
antisymmetry is impossible. Bosons have symmetric pairwise
wavefunctions (you can swap two bosons, and nothing changes), hence it
is possible to have more than one boson in the same state.

I'd have to go back to my class notes of QM to check this of course,
just speaking from 35+ years ago when I last studied this.

On Fri, Apr 03, 2020 at 08:16:51AM -0700, Lawrence Crowell wrote:
> It is reasonable to state the Pauli exclusion principle is a postulate on its
> own. There are though other possibilities. With supersymmetry, parafermions,
> bosonization and now fermionization of bosons the role of the PEP is not
> entirely certain. 
>
> LC
>
> On Thursday, April 2, 2020 at 8:09:23 PM UTC-5, Alan Grayson wrote:
>
>     Does the Pauli's Exclusion Principle have a similar status in QM as Born's
>     rule; namely, an empirical fact not derivable from the postulates of QM?
>     TIA, AG
>
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[Bruno Marchal]

On 4 Apr 2020, at 10:59, Bruce Kellett <bhkel...@gmail.com> wrote:

On Sat, Apr 4, 2020 at 7:36 PM Russell Standish <li...@hpcoders.com.au> wrote:

I thought the principle came from antisymmetry of fermionic pairwise
wavefunctions. If two fermions occupied the same state, then
antisymmetry is impossible. Bosons have symmetric pairwise
wavefunctions (you can swap two bosons, and nothing changes), hence it
is possible to have more than one boson in the same state.

As I recall it, this is completely right. I think it all goes back to the nature of the 4-component spinors of Dirac theory -- rotation by 360 degrees changes the sign, necessitating the antisymmetric nature of the quantum state. Fermi-Dirac statistics, and as has been said, the fundamental spin-statistics theorem.

That’s what I recall too, notably from my reading of the Feynman Lecture on Quantum Mechanics. It is clearer in the relativistic setting perhaps, I am not sure.

Bruno

Bruce 

I'd have to go back to my class notes of QM to check this of course,
just speaking from 35+ years ago when I last studied this.

On Fri, Apr 03, 2020 at 08:16:51AM -0700, Lawrence Crowell wrote:
> It is reasonable to state the Pauli exclusion principle is a postulate on its
> own. There are though other possibilities. With supersymmetry, parafermions,
> bosonization and now fermionization of bosons the role of the PEP is not
> entirely certain. 
>
> LC
>
> On Thursday, April 2, 2020 at 8:09:23 PM UTC-5, Alan Grayson wrote:
>
>     Does the Pauli's Exclusion Principle have a similar status in QM as Born's
>     rule; namely, an empirical fact not derivable from the postulates of QM?
>     TIA, AG

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