Renormalisation constants in QED

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SUMMARY

The discussion focuses on the derivation of renormalisation constants in Quantum Electrodynamics (QED) using the textbook "An Introduction to Quantum Field Theory" by Peskin and Schroeder. The key points include the choice to absorb the Z_3 constant in the photon wavefunction instead of the electron charge, and the reasoning behind separately including Z_1 and Z_2 in electron charge renormalisation despite their cancellation, as established by the Ward identity. These concepts are critical for understanding the nuances of QED renormalisation.

PREREQUISITES
  • Familiarity with Quantum Electrodynamics (QED)
  • Understanding of renormalisation concepts
  • Knowledge of the Ward identity in quantum field theory
  • Experience with Peskin and Schroeder's textbook
NEXT STEPS
  • Study the derivation of renormalisation constants in QED using Peskin and Schroeder
  • Explore the implications of the Ward identity on renormalisation
  • Investigate the physical significance of Z_1, Z_2, and Z_3 in QED
  • Review advanced topics in quantum field theory related to gauge invariance
USEFUL FOR

Students and researchers in theoretical physics, particularly those focusing on Quantum Electrodynamics and renormalisation techniques. This discussion is beneficial for anyone seeking a deeper understanding of the mathematical framework of QED.

blackie1008
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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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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.
 

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