24. Proving Lande g-Factor gₑ = 2 from the Dirac Equation | QFT | Dr. Jamil Aslam

December 12, 2025

Course Instructor:
Dr. Muhammad Jamil Aslam
(Professor, Department of Physics, Quaid-i-Azam University, Islamabad)

Timestamps:

Recap
00:00 Schrödinger → KG → Dirac
05:23 Goal: Showing that the Dirac equation predicts the Landé g-factor = 2
06:06 Recap: The Dirac equation in an EM field

Chiral Representation
08:10 Representation invariance of the Dirac equation
09:26 Chiral (Weyl) representation of gamma matrices
10:38 Notation in Peskin & Schroeder
12:30 Decomposition of Dirac spinor ψ into left and right chiral components
16:04 Rewriting the previous result in matrix form

A Special Case
22:50 For A = (0, Ā), Ā is time-independent
26:08 Klein-Gordon equation retrieved!
28:14 Relativistic → Non-relativistic
37:28 Schrödinger equation retrieved!
42:24 (∇ − ieĀ)²
43:58 Coulomb & Lorenz Gauge
46:50 −ie Ā·∇ = (e/2) B̄·L̄
49:26 (e/2) σ̄ · B̄ = (e/2) 2S̄ · B̄
50:59 gₑ = 2 yay!!
（＾＾）人（＾＾）

Discussion
52:11 New Physics: Muon (g - 2) anomaly & higher-order loop effects
56:18 Other proofs of QFT
56:57 General relativity, gravity, graviton & other grandiose stuff
1:03:30 Up Next: Solutions to the Dirac Equation → Auxiliary Coefficients → Fermion Fields → Fermions
1:03:53 Question: How do we know that the solutions to the Dirac equation describe fermions?
1:04:30 Is it really a physics class without a discussion on the nature of spin? XD
1:08:13 The limits of our perception

Solutions to the Dirac Equation
1:08:57 Inserting plane-wave ansatz into the Dirac equation
1:12:40 (p/ – m)u(p) = 0
1:13:57 Conjugate: [(p/ – m)u(p)]† = 0
1:17:35 ū ≡ u† γ⁰
1:18:36 γ⁰ (γ^μ)† γ⁰ = γ^μ
1:19:55 Dirac spinors: u(p), ū(p)
1:22:40 Where the course will end


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