Help me in QTF theory(t'Hoof's method)?

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In summary, the conversation discusses using dimensional regularization (t'Hoof method) to solve the problem of infinite mass of photons and the violation of Ward identity. By restricting to considering the one loop self energy of photon approximation, the order of divergence can be reduced from quadratic (at 4 dimensions) to logarithmic (at 2 dimensions). The individual asking for help does not understand why reducing the dimensions of the integral leads to a decrease in the order of divergence. They believe that the decrease in one dimension should result in a decrease of one order in power, not a change to logarithmic divergence. However, they have since found the answer in the Mandl&Shaw book on quantum field theory (QTF) in section
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ndung200790
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Please help me this problem:
Considering dimensional regularization(t'Hoof method) to solve the infinite mass of photon and so that the violation of Ward identity problem,we restrict to consider one loop self energy of photon aproximation(in Schroder and Peskin's QTF book,7.5 chapter 7).I don't understand why reducing the 4 space-time dimensions to 2 dimensions( the dims of loop integral) then the order of divergence reduce from quadratic divergence(at 4 dims) to logarithmic divergence(at 2 dims).Because it seem to me by decreasing 1 dimension of integral,the divergence decreases by 1 order in power,so it would not be logarithmic divergence at 2 dimensions integral.
Thank you very much in advanced.
 
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I have just found out the answer in 10.1.2 in QTF book of Mandl&Shaw
 

1. What is QTF theory?

QTF theory, or the Quantum Theory of Fields, is a theoretical framework used to describe the dynamics of quantum fields. It combines the principles of quantum mechanics and special relativity to explain the behavior of subatomic particles and their interactions.

2. Who developed t'Hoof's method?

t'Hoof's method, also known as the t'Hoof's-Veltman method, was developed by Dutch physicist Gerard 't Hooft. He received the Nobel Prize in Physics in 1999 for his work on this method and his contributions to the understanding of the strong nuclear force.

3. What is the purpose of t'Hoof's method in QTF theory?

t'Hoof's method is used in QTF theory to help calculate the quantum corrections to the behavior of particles. It is a mathematical tool that allows for the calculation of Feynman diagrams, which represent the possible interactions between particles.

4. How does t'Hoof's method differ from other methods in QTF theory?

t'Hoof's method differs from other methods in QTF theory in that it uses a mathematical technique called dimensional regularization, which involves working with equations in a different number of dimensions than the physical world. This allows for the cancellation of divergences and the calculation of finite results.

5. What are the practical applications of t'Hoof's method in QTF theory?

t'Hoof's method has been used to make precise calculations and predictions in the field of particle physics, particularly in the study of the strong nuclear force. It has also been used to help understand and test other theories, such as the Standard Model of particle physics and the theory of quantum electrodynamics.

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