Physics 424 Lecture 16 - The Feynman Rules for QED

Q: What is the purpose of the Feynman rules for QED in this lecture?

They provide a recipe for constructing an amplitude from a Feynman diagram by turning diagram elements into algebraic factors.

Q: What are the three steps to build a QED amplitude from a diagram?

Draw the diagram with the minimum number of vertices, label four-momenta with conservation at each vertex, then combine vertex factors, internal propagators, and external wavefunctions.

Q: Why must external line factors be placed on the outside?

Because the vertex factors and fermion propagators involve matrices, while the final amplitude must be a scalar, requiring external factors to sit outside the matrix products.

Oct 25, 2026

Uploaded by Ezra

Physics 424 Lecture 16 presents a structured recipe for constructing QED amplitudes from Feynman diagrams. It outlines three steps: draw the diagram with the minimum number of vertices, label each line’s four-momentum while enforcing four-momentum conservation at every vertex, and build the amplitude from vertex factors, propagators for internal lines, and wavefunctions for external lines. The lecture further clarifies photon and fermion propagator structure, gauge conditions such as Coulomb gauge and related Lorentz condition properties, and explains why external line factors must be placed outside to yield a scalar amplitude.

LanguageEnglish

CategoryTechnology

FormatPDF

Pages31

Reading Time1 h 18 min

AccessFree to download

The Feynman Rules for QED

Constructing amplitudes from diagrams

Vertex factors, propagators, and external line factors

Photon and fermion propagators

Feynman rules for QED The Feynman Rules for QED Setting up Amplitudes Casimir's Trick Trace Theorems Slides from Sobie and Blokland 􀀀 􀀀 􀀀 􀀀 Physics 424 Lecture 16 Page 1 | Electrons and positrons | | --- | | spinors
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✙ | Physics 424 Lecture 16 Page 2 Photons ✏ ☞ ✟ ☛ % $ \# ! ✤ ✣ ✢ ✑ ✏ ✜ ✟ ☛ ✛ Lorentz condition orthogonality normalization Coulomb gauge and Completeness ✗ ☞ - ✏ * ☞ ☞ ✟ ✍ * , ✒ ✑ ✑ * ) ✏ ✝ ( ☎ ✒ & ✄ % % ✑ ✬ ✟ ✒ ✏ ✑ ✝✗✄ ✑ ✒ ✝☎✄ ☛ ☛ % ☞ ☛ & %✝ &% ✑ ✟☎☛ ☛ ✄✖% ☛% ✕% ✙ % ✁ ✁ ✁ ✁ ✁ Physics 424 Lecture 16 Page 3 The Feynman Rules for QED The Feynman rules provide the recipe for constructing an amplitude from a Feynman diagram. Step 1: For a particular process of interest, draw a Feynman diagram with the minimum number of vertices. There maybe more than one. . ✁ 4 ☞ / 1 ✣ 3 ☞ / ✤ ✣ ✠ ✗ ☞ / 1 ✣ ✖ ☞ / ✤ ✣ Physics 424 Lecture 16 Page 4 The Feynman Rules for QED Step 2: For each Feynman diagram, label the four-momentum of each line, enforcing four-momentum conservation at every vertex. Note that arrows are only present on fermion lines and they represent particle 􀀃ow, not momentum. 4 ☞ / 1 ✣ 3 ☞ / ✤ ✣ ✁ ✠ ✗ ☞ / 1 ✣ ✖ ☞ / ✤ ✣ Physics 424 Lecture 16 Page 5 Step 3: The amplitude depends on 1. Vertex factors 2. Propagators for internal lines 3. Wavefunctions for external lines 􀀀 Physics 424 Lecture 16 Page 6 Vertex Factors Every QED vertex, contributes a factor of . is a dimensionless coupling constant and is related to the 􀀂ne-structure constant by 􀀀 5 5 6 < 6 78: >= : 8 􀀀 Physics 424 Lecture 16 Page 7 | Propagators | | --- | | Each internal photon connects two vertices of the form and , so we should expect the photon propagator to contract the indices and .
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􀀀 | Physics 424 Lecture 16 Page 8 External Lines Since both the vertex factor and the fermion propagators involve matrices, but the amplitude must be a scalar, the external line factors must sit on the outside. Work backwards along every fermion line using: @ L @ 􀀀 􀀀 | | | | | | | | --- | --- | --- | --- | --- | --- | | in
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5 | | | --- | --- | | | 6 | | 5 | | Physics 424 Lecture 16 Page 10

FAQs

What is the purpose of the Feynman rules for QED in this lecture?

They provide a recipe for constructing an amplitude from a Feynman diagram by turning diagram elements into algebraic factors.

What are the three steps to build a QED amplitude from a diagram?

Draw the diagram with the minimum number of vertices, label four-momenta with conservation at each vertex, then combine vertex factors, internal propagators, and external wavefunctions.

Why must external line factors be placed on the outside?

Because the vertex factors and fermion propagators involve matrices, while the final amplitude must be a scalar, requiring external factors to sit outside the matrix products.

Oct 25, 2026

Uploaded by Ezra