Renormalization Theory: Solving Infinite Series

[eljose79]

Where could i find a good introductionto renormalization theory ? ( i have a degree in physics but i do not know about renormalization).
In fact i have some questions:
Let us suppose we have the series:

f(g)=a0+a1g+a2g**2+.. where g is the coupling constant and a0,a1,a2,a3..an are numerical values (real or complex)

then just suppose that some of them a1,a5,a7 for example give an infinite value...how could you re-arrange the series or what trick is used to remove these infinites

If all the an where infinite ..how could you remove them?..

 

[ahrkron]

Many QFT books have good accounts of renormalization. I like Peskin and Schroeder. M. Kaku's is good also.

If you don't have access to them, you can also take alook at the online book used for the thread on QFT here in the forums.

 

[selfAdjoint]

Note that many texts, like P&S, use the word renormalization in a different sense than it used to be. What used to be called renormalization is now called regularization (as in "Pauli-Villars regularization" and "Dimensional regularization"). The result of regularization is to leave an undetermined quantity in the integrals as the price for eliminationg the ultraviolet divergences. After the integrals are formed the process now called renormalization happens, to remove the undetermined quantity by folding it into an overall constant.

 

[jeff]

Originally posted by eljose79
Where could i find a good introductionto renormalization theory ? ( i have a degree in physics but i do not know about renormalization).

For clear, uncomplicated introductions which emphasize the conceptual aspects see Zee's new book Quantum theory in a nutshell



and Sidney Coleman's famous collection of lectures Aspects of symmetry



They're each worth every penny (if you want to buy).

Originally posted by eljose79
Let us suppose we have the series:

f(g)=a0+a1g+a2g**2+.. where g is the coupling constant and a0,a1,a2,a3..an are numerical values (real or complex)

then just suppose that some of them a1,a5,a7 for example give an infinite value...how could you re-arrange the series or what trick is used to remove these infinites

If all the an where infinite ..how could you remove them?..

Before I answer your question, it would help me if you could tell me whether you have any familiarity with the basics of feynman diagrams and perturbation theory in QFT (not including renormalization).

Originally posted by selfAdjoint
What used to be called renormalization is now called regularization

[?]

 

[eljose79]

reply

i gae feynmann graphs and integrals in the last course altough we did not achieve the problem of renormalization i would like to know an introduction to it.in the math and physical aspects of it and know if all the integrals diverge as (dn**v)p**v-1 (1)( i think this is made to know the grade of divergence...

the problem is...why if a theory is ot renormalizable can not we derivate to get the integrals to be convergent supposing they diverge as (1), could we point an introductory remark on renormalization (a paper to introduce the math and physics of it without include the renormalization group..

 

[vanesch]

QFT course...

BTW, if you're interested in studying Peskin and Schroeder, I think that Patrick Labelle will start his course on QFT again (on the same site where I start my non-relativistic quantum mechanics course, www.superstringtheory.com). If people are interested, send me an e-mail (I'll transmit it to Patrick Labelle, but I don't want to put his e-mail directly on this forum without his permission).