Why is the Electron Self-Energy Important in QFT Theory?

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In summary, they say that we can sum the left hand side to have the right hand side because the left is a geometric series. However, they warn that the calculation is done before the making of renormalization, and that the result may not be valid.
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ndung200790
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Please teach me this:
In QTF theory book of Peskin&Schroder they say:Call 1PI the one particle irreducible diagram,so Fourier two-point correlation function can write:
i/(gamma(vector).p-m0) +i/(gamma.p-m0)(1PI/(gamma.p-m0) +i/(gamma.p-m0)square(1PI/(gamma.p-m0))...=i/(gamma.p-m0-1PI).
They say that we can sum the left hand side to have the right hand side because the left is a geometric serie.But I don't understand why we can sum while we don't know 1PI/(gamma.p-m0) being smaller than 1 or not.Another worrying is that the calculation is done before the making renormalization and QED being asymtotic theory.
Thank you very much in advanced.
 
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  • #2
ndung200790 said:
Please teach me this:
In QFT theory book of Peskin&Schroder they say:Call 1PI the one particle irreducible diagram,so Fourier two-point correlation function can write:
i/(gamma(vector).p-m0) +i/(gamma.p-m0)(1PI/(gamma.p-m0) +i/(gamma.p-m0)square(1PI/(gamma.p-m0))...=i/(gamma.p-m0-1PI).
They say that we can sum the left hand side to have the right hand side because the left is a geometric series. But I don't understand why we can sum while we don't know 1PI/(gamma.p-m0) being smaller than 1 or not.Another worrying is that the calculation is done before the making renormalization and QED being asymptotic theory.

Using 1+z+...+z^n+... = 1/(1-z) without bothering about convergence is called formal manipulation. Note that the formula is valid in the field of formal power series in z. Quantum field theory is full of such formal manipulations. After sufficiently skilful such manipulations and approximations one usually arrives at something (called ''renormalized'') where one can insert a particular value of z and get meaningful results. This can be justified in many cases by means of expansions of analytic functions, so one hopes that it also gives valid results when such justifications are too hard to come by (as in QED).
The proof is then by comparison with experiment rather than by rigorous mathematics.
 
  • #3
I am profound grateful the kind helping of Prf.A Neumaier
 

FAQ: Why is the Electron Self-Energy Important in QFT Theory?

What is the Electron Self-Energy in QFT Theory?

The Electron Self-Energy is a fundamental concept in Quantum Field Theory (QFT) that describes the interaction of an electron with its own electromagnetic field. In other words, it is the energy that the electron gains or loses due to its interactions with the virtual particles present in the vacuum.

Why is the Electron Self-Energy Important in QFT Theory?

The Electron Self-Energy is important in QFT theory because it plays a crucial role in understanding the behavior of particles at the quantum level. It affects the mass, charge, and other properties of the electron, and without accounting for it, our understanding of particle interactions and phenomena would be incomplete.

How does the Electron Self-Energy affect the Mass of the Electron?

The Electron Self-Energy affects the mass of the electron by contributing to its rest mass. The self-energy of an electron is infinite, but QFT calculations allow us to renormalize this value to a finite value, which is added to the rest mass of the electron. This explains why the mass of the electron is not constant and can vary slightly in different conditions.

What is the Significance of the Electron Self-Energy in Particle Interactions?

The Electron Self-Energy is significant in particle interactions because it contributes to the stability and lifetime of particles. For example, the self-energy of the electron affects its ability to interact with other particles, such as photons, and can impact the outcome of these interactions.

How is the Electron Self-Energy Calculated in QFT?

The Electron Self-Energy is calculated using perturbation theory, which involves breaking down the interaction between the electron and its own field into smaller, solvable parts. These calculations can then be used to determine the self-energy and its effects on the electron's properties. However, the self-energy is an infinite quantity, and renormalization techniques are used to obtain a finite value that can be used in calculations.

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