Re: Pauli's Exclusion Principle

[Bruno Marchal]

> On 4 Apr 2020, at 10:59, Bruce Kellett  wrote:
> 
> On Sat, Apr 4, 2020 at 7:36 PM 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.
> 
> 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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Re: Pauli's Exclusion Principle

[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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>
>
>
> -- 
>
>  
>
> Dr Russell StandishPhone 0425 253119 (mobile) 
> Principal, High Performance Coders hpc...@hpcoders.com.au 
>  
>   http://www.hpcoders.com.au 
>  
>
>

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Re: Pauli's Exclusion Principle

[Bruce Kellett]

On Sat, Apr 4, 2020 at 7:36 PM 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.
>

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

>
> 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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Re: Pauli's Exclusion Principle

[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.

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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Dr Russell StandishPhone 0425 253119 (mobile)
Principal, High Performance Coders hpco...@hpcoders.com.au
  http://www.hpcoders.com.au


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Re: Pauli's Exclusion Principle

['Brent Meeker' via Everything List]

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


Brent

On 4/3/2020 4:25 AM, John Clark wrote:
On Thu, Apr 2, 2020 at 9:09 PM 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/


Yes.

John K Clark

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Re: Pauli's Exclusion Principle

[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

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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Re: Pauli's Exclusion Principle

[John Clark]

On Thu, Apr 2, 2020 at 9:09 PM 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*
>

Yes.

John K Clark

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