Problem in understanding the Isospin

[neelakash]

I am a general reader.I found in a book:"Three quarks with I=(1/2) can combine to form I_tot=(1/2) [did not understand] or (3/2) [OK].I_tot = (1/2) gives the nucleons while I_tot = (3/2) forms the baryons.

Now,using u and d isospin doublet,I expressed the baryons:uuu,uud,udd,ddd.And found that I_tot= (3/2).It is OK.

But I cannot see how I_tot=(1/2) [I have not considered I_3 component,however] for nucleons.Forming the doublet of p and n I saw that they conforms to uud and udd (which I got in baryons,too).So,what makes these different from them?

 

[Barmecides]

I am a general reader.I found in a book:"Three quarks with I=(1/2) can combine to form I_tot=(1/2) [did not understand] or (3/2) [OK].I_tot = (1/2) gives the nucleons while I_tot = (3/2) forms the baryons.

Now,using u and d isospin doublet,I expressed the baryons:uuu,uud,udd,ddd.And found that I_tot= (3/2).It is OK.

But I cannot see how I_tot=(1/2) [I have not considered I_3 component,however] for nucleons.Forming the doublet of p and n I saw that they conforms to uud and udd (which I got in baryons,too).So,what makes these different from them?

Nucleons are baryons.
You can assign to up quark isospin_3 = +1/2 and to down quark isospin_3 = -1/2
Then :
- if you consider I_tot = 1/2, possible values of I_3 are +1/2 and -1/2 (as spin or angular momentum in quantum mecanics) and these values correspond to proton (uud) and neutron (udd)
- if you consider I_tot = 3/2, possible values of I_3 are [-3/2, -1/2, 1/2, 3/2] and they correspond to different Delta baryons ddd, ddu, duu and uuu

Hope it helps.

 

[Norman]

Have you studied the formal theory of the addition of angular momentum in Quantum Mechanics? Isospin acts just like Spin.

 

[nrqed]

I am a general reader.I found in a book:"Three quarks with I=(1/2) can combine to form I_tot=(1/2) [did not understand] or (3/2) [OK].I_tot = (1/2) gives the nucleons while I_tot = (3/2) forms the baryons.

Now,using u and d isospin doublet,I expressed the baryons:uuu,uud,udd,ddd.And found that I_tot= (3/2).It is OK.

But I cannot see how I_tot=(1/2) [I have not considered I_3 component,however] for nucleons.Forming the doublet of p and n I saw that they conforms to uud and udd (which I got in baryons,too).So,what makes these different from them?

To understand the I=1/2 case, some knowledge of quantum mechanics is necessary (addition of angular momenta). If you have done some quantum mechanics, just think fo combining two spin 1/2 into the symmetric S=1 states and the antisymmetric S=1/2 state. Isospin follows the same rule.

EDIT: Oops, I posted this without seeing Norman's reply which is basically identical to mine.

 

[neelakash]

Thank you all...
You might laugh...but I have just started qm course.
Till now I have read 1D problems in wave-mechanics formalism...

So,I have to read a lot more.I was interested and was trying these with intuitive ideas served by Hyperphysics and Wikipedia.It's not really worthful.
Please help me in following regards:

(i)Is wave mechanics formalism OK to have a grip on Standard model? I say this because I have to use group formalism...and I think the matrix mechanics formalism will be preferable...
(ii)Can you please refer me to some webpage/link/lecture notes that will help me to understand the Standard Model?I do not want hyperphysics/particle adventure types page;something that will be mathematical and comprehensible as well.
Currently I have some books...they start from very advanced mathematics and topics like these(I have posted here).So,these really do not help.I have a 2nd choice for Brian Martin's book.I found it more comprehensible...but it possibly does not develops the theory for the Standard Model...

 

[malawi_glenn]

Well its quite hard to understand Standard model without higher knowledge in QM, such as relativistic (Dirac and Klein Gordon eq). Either the book is fenomenological, or requires rel QM. But Martins "particle physics" (blue book, Wiley) Is one of the few books i know that treat particle physics without presumption that the reader knows rel QM. Also Griffiths is not that dense as many other.

After you are done with wave mechanics, you might want to learn more advanced QM with Dirac formalism (such books as Sakurai Modern QM might be good).

But to understand standar model, you need a lot background, sorry, I am in the same situation ;) I am now taking courses in more advanced QM then I will have rel QM, then finally Elementary particle phyics =) So my suggestion is that you learn how to walk before you try running.

 

[neelakash]

malawi_glenn, you are right.Brian Martin deals with the topic brilliantly.So far,I did not have any problem in qualitative understamding.
However,to do the subject one really cannot skip the step by step way.

 

[malawi_glenn]

malawi_glenn, you are right.Brian Martin deals with the topic brilliantly.So far,I did not have any problem in qualitative understamding.
However,to do the subject one really cannot skip the step by step way.

Things will only get clearer then :) Next step you can go to is Griffiths book, it will be re-released in febrary 2008 I think (new edition, the last one is from 1987 i think..)


https://www.amazon.com/dp/0471603864/?tag=pfamazon01-20

http://eu.wiley.com/WileyCDA/WileyTitle/productCd-3527406018.html


Also "Nuclear and Particle Physics: An Introduction" by Brian Martin is also a good book I've heard, but his blue book should contain all that this one does.

 

[neelakash]

I see...