Understanding Counter Term Renormalization in Quantum Field Theory

In summary, the conversation discussed the topic of counter term renormalization in QFT calculations. The insertion of mass counter terms in one loop diagrams is equivalent to taking the derivative of the one loop diagram multiplied by the mass counter term. This is explained in the perturbative renormalization theory, specifically in Chapter 5 and Section 5.11 about the renormalization group. The person also recommended a book by Mccomb for beginners in this subject.
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mandy96
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Currently, I am reading about counter term renormalization used to eliminate the infinities in the loop calculations involved in QFT calculations. I found somewhere that the insertion of mass counter terms in one loop diagrams is equivalent to the derivative of one loop diagram multiplied with mass counter term. I am not getting this point.. If anybody can help me with that it would be very helpful.. Thanks..
For reference : arXiv:hep-ph/9406431 equation no. (3.6 ) in this..
Currently, I am reading about counter term renormalization used to eliminate the infinities in the loop calculations involved in QFT calculations. I found somewhere that the insertion of mass counter terms in one loop diagrams is equivalent to the derivative of one loop diagram multiplied with mass counter term. I am not getting this point.. If anybody can help me with that it would be very helpful.. Thanks..
For reference : arXiv:hep-ph/9406431 equation no. (3.6 ) in this..
 

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Have a look at my QFT manuscript:

https://itp.uni-frankfurt.de/~hees/publ/lect.pdf

In Chpt. 5 you find perturbative renormalization theory. The discussion of different renormalization schemes and how the derivatives wrt. mass to define the counter terms come into the game is in Sect. 5.11 about the renormalization group.
 
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vanhees71 said:
Have a look at my QFT manuscript:

https://itp.uni-frankfurt.de/~hees/publ/lect.pdf

In Chpt. 5 you find perturbative renormalization theory. The discussion of different renormalization schemes and how the derivatives wrt. mass to define the counter terms come into the game is in Sect. 5.11 about the renormalization group.
Thanks... I will surely take a look...
 
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Related to Understanding Counter Term Renormalization in Quantum Field Theory

What is counter term renormalization?

Counter term renormalization is a mathematical technique used in quantum field theory to remove divergences in calculations of physical quantities. It involves adding and subtracting terms in the equations to cancel out the infinities and obtain finite results.

Why is counter term renormalization necessary?

Counter term renormalization is necessary because in quantum field theory, calculations often lead to infinite values. These infinities arise due to the fact that quantum mechanics and special relativity do not play well together. Counter term renormalization allows us to obtain meaningful and finite results from these calculations.

How does counter term renormalization work?

Counter term renormalization works by adding and subtracting terms in the equations to cancel out the infinities. This is done in a systematic way, using the principles of quantum field theory and perturbation theory. The added terms, known as counter terms, have adjustable parameters that can be chosen to precisely cancel out the infinities.

What are the limitations of counter term renormalization?

Counter term renormalization is not a perfect solution and has its limitations. It can only remove divergences up to a certain order, and higher order corrections may still lead to infinities. Additionally, the choice of counter terms is not unique and can affect the final results. Furthermore, counter term renormalization does not provide a physical explanation for why infinities arise in quantum field theory calculations.

What are some applications of counter term renormalization?

Counter term renormalization is used extensively in theoretical physics, particularly in quantum field theory and particle physics. It is essential for making precise predictions and calculations in these fields. Additionally, it has been applied to other areas of physics, such as condensed matter physics and statistical mechanics, to deal with infinities that arise in these systems.

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