QED, chapter 4 P&S page 125 (Coulomb Potential)

Thread starter Pouramat
Start date Jan 10, 2021
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Coulomb potential Gamma function Potential Qed

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SUMMARY

The discussion centers on the properties of Dirac spinors in quantum electrodynamics (QED), specifically in chapter 4 of the text. The equation $$\bar u(p') \gamma^i u(p) = u^\dagger(p') \gamma^0 \gamma^i u(p)$$ is established as a fundamental relationship. When the momentum vectors are equal (##p = p'##), the identity $$u^\dagger(p) u(p) = 2m \xi^\dagger \xi$$ is utilized to derive properties of the spinors. The query focuses on determining the form of the spinor ##u(p)## when the momentum ##\vec{p}## is zero.

PREREQUISITES

Understanding of Dirac spinors and their properties
Familiarity with quantum electrodynamics (QED)
Knowledge of gamma matrices and their algebra
Basic concepts of relativistic quantum mechanics

NEXT STEPS

Study the derivation of Dirac spinors in QED
Learn about the implications of momentum space in quantum field theory
Explore the role of gamma matrices in particle physics
Investigate the physical interpretation of spinors at rest (##\vec{p}=0##)

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This discussion is beneficial for theoretical physicists, students of quantum mechanics, and anyone studying quantum field theory, particularly those focusing on the properties of fermions in QED.

Jan 10, 2021

Pouramat

Homework Statement: In section Coulomb Potential stated that: "You can easily verify that the other terms mentioned below vanish if ##p = p' = o##"
which we are working in nonrelativistic limit

Relevant Equations: $$\bar u(p') \gamma^i u(p)$$

$$\bar u(p') \gamma^i u(p) = u^\dagger(p') \gamma^0 \gamma^i u(p)$$
if ##p = p'## we can use
$$u^\dagger(p) u(p) = 2m \xi^\dagger \xi$$
but how can we conclude the statement?