Renormalisation constants in QED

In summary, the renormalization constants in QED, specifically Z_1 and Z_2, are chosen to be absorbed in the electron charge and photon wavefunction, respectively. This is because they cannot be absorbed into each other and all terms are needed in the renormalization process. Additionally, although the Ward identity proves Z_1=Z_2, they are still included separately in the electron charge renormalisation as all terms are required for the process to work. This can be found in Peskin and Schroeder on pages 330-331.
  • #1
blackie1008
5
0
Hi,

I have been deriving the renormalisation constants in QED as part of my project. I have been using Peskin and Schroeder. I am a bit confused with a couple of things and was wondering if anyone could please help!

Firstly, why do we chose not to absorb the Z_3 constant in the electron charge but rather the photon wavefunction?

Secondly, why, when we have used the Ward identity to prove Z_1=Z_2 do we then include them separately in the electron charge renormalisation when they just cancel?

(This is around about p330-331 in Peskin and Schroeder)
 
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  • #2
blackie1008 said:
Hi,

I have been deriving the renormalisation constants in QED as part of my project. I have been using Peskin and Schroeder. I am a bit confused with a couple of things and was wondering if anyone could please help!

Firstly, why do we chose not to absorb the Z_3 constant in the electron charge but rather the photon wavefunction?

Secondly, why, when we have used the Ward identity to prove Z_1=Z_2 do we then include them separately in the electron charge renormalisation when they just cancel?

(This is around about p330-331 in Peskin and Schroeder)
One can absorb terms only in terms of the same form, and one needs all these terms.
 

1. What is the role of renormalisation constants in QED?

Renormalisation constants in QED are used to remove divergences in the theory and ensure that physical observables are finite. They are crucial in making predictions and calculations in quantum electrodynamics (QED) accurate and meaningful.

2. How are renormalisation constants calculated in QED?

The calculation of renormalisation constants in QED involves a complex mathematical process known as perturbation theory. This involves breaking down the problem into smaller, more manageable parts and using mathematical techniques to solve them.

3. What is the physical significance of renormalisation constants in QED?

Renormalisation constants in QED have a physical significance as they represent the strength of the interaction between charged particles and the electromagnetic field. They also play a role in determining the values of physical observables such as particle masses and coupling constants.

4. How do renormalisation constants affect the predictions of QED?

Renormalisation constants play a critical role in making accurate predictions in QED. They allow for the removal of infinities in the theory and ensure that calculated values for physical observables are finite and realistic. Without renormalisation constants, predictions in QED would not match experimental results.

5. Are renormalisation constants unique to QED?

No, renormalisation constants are also used in other quantum field theories to remove infinities and ensure the accuracy of predictions. However, the specific values of the renormalisation constants in QED are unique to this particular theory and are derived through experimental measurements and calculations.

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