Fermions vs Bosons: Low Temp Effects

[Ilmrak]

why is that at relatively low temperature bosons can occupy the same state while the fermions cannot?
and how does we macroscopically see the effects of bosons (with explanations)?

a theoretical answer is preferable

By definition fermion fields creation and destruction operators satisfies

<br /> \{a_\alpha^\dagger, a_\beta^\dagger\}= 0\; , \\<br /> \{a_\alpha,a_\beta\}= 0\; ,\\<br /> \{a_\alpha^\dagger, a_\beta\}= \delta_{\alpha,\beta} \; ,<br />

while boson fields creation and destruction operators satisfies

<br /> \left[a_\alpha^\dagger, a_\beta^\dagger\right]= 0\; ,\\<br /> \left[a_\alpha,a_\beta\right]= 0\; ,\\<br /> \left[ a_\alpha^\dagger, a_\beta\right]= \delta_{\alpha,\beta}\; .<br />

These (anti-)commutation rules implies that two fermions can't be in the same state (a_\alpha^\dagger a_\alpha^\dagger= 0) while two bosons can (a_\alpha^\dagger a_\alpha^\dagger \neq 0).

It can be shown that either a particle is a boson or it's a fermion, there isn't a third option.

Furthermore the Spin-Statistic theorem states that a particle with integer spin has to be a boson, while a semi-odd spin particle has to be a fermion.

Macroscopically a system of bosons can show superfluidity, while maybe the most known examples of the Fermi statistic are neutron stars.

[...] Very macroscopically, you need only look to neutron (boson) stars vs White dwarf (fermion) stars.[...]

Neutrons are fermions!

getting higgs theory into the picture, i think that higgs field has something more to do than adding the mass, there must some asymmetry before the particle could take their statistical properties but i am unable to find the event that will bring sufficient asymmetry.

There's really no need to invoke the Higgs field to explain how particles gains their statistical properties.
Actually your sentence sounds as a non-sense, as the Higgs is a boson (spin zero) and so statistics is needed to describe even the Higgs field.
Note that Fermi and Bose statistics reflects symmetries, not asymmetries.

can you give me an example where matter-antimatter anhilation is not involved in producing a boson fron fermions or vice versa
and the boson produced in the process must have some physical properties instead of being an energy packet.

All bosons has physical properties.
However, a process you may like is

e^- \;\bar{\nu}_e \rightarrow W^- \; ,

where e^- and \bar{\nu}_e are fermions and W^- is a boson.

is it necessary that the bosons will always play the role of force carrier?

No it's not necessary.
In the standard model there is exactly one boson that is not a gauge boson and so doesn't carry a force: the Higgs boson.

I hope this could help a bit.

Ilm

 

[mpv_plate]

is it necessary that the bosons will always play the role of force carrier?

Two bosons can scatter of each other thanks to intermediate fermions. That is the case of photon-photon scattering which happens due to interaction via the virtual electron-positron pair. However I am not sure if this is what you asked for.

 

[Simon Bridge]

is it necessary that the bosons will always play the role of force carrier?

No. It is the other way around: in the standard model, the gauge fields give rise to force carriers which are bosons.
Not all interactions need be mediated by bosons.
Not all spin 0 objects are force carriers.

Now please answer the question posed by dalespam: "what do you mean by field behaviour?"

We cannot help you if you will not answer questions.

 

[nouveau_riche]

No. It is the other way around: in the standard model, the gauge fields give rise to force carriers which are bosons.
Not all interactions need be mediated by bosons.
Not all spin 0 objects are force carriers.

Now please answer the question posed by dalespam: "what do you mean by field behaviour?"

We cannot help you if you will not answer questions.

what i meant to say was that if a fermion is changing into a boson that is a carrier of force, the field generating fermion has itself transformed into the carrier under some conditions, this could help to figure the fermion-boson relationship.

 

[Ilmrak]

what i meant to say was that if a fermion is changing into a boson that is a carrier of force, the field generating fermion has itself transformed into the carrier under some conditions, this could help to figure the fermion-boson relationship.

I think it may be worth to remark that the bosonic or fermionic nature of a field is a symmetry property of that field. A field would have such a symmetry even if it was the only field of your theory, it doesn't depend on the other fields and in particular it doesn't depend on the interaction with other particles.

So I think you should change a bit your perspective on this topic, maybe trying to formulate different kind of questions to better understand bosons and fermions.

Ilm