Скачать или смотреть 22. The Dirac Equation: Motivation & Derivation | QFT | Dr. Jamil Aslam

December 10, 2025

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


Timestamps:

Motivation for the Dirac Equation
00:00 Recap: Scalar Field Theory
02:50 An issue with the Klein-Gordon equation
04:00 Derivation of Continuity Equation for Klein-Gordon
06:26 Question: Why would the KG equation hold for φ*(x)?
07:15 Derivation continued . . .
11:18 Defining J vector
11:42 Defining ρ
12:11 The Continuity Equation
12:56 Evaluating ρ for a plane wave solution
16:37 ρ is not our usual ρ
17:41 Caught in a dilemma! What now?
18:46 Temporal ρ & spatial J
22:29 What do we do with negative energy solutions now?!
24:27 A question we should have asked but didn't
25:19 Inspired by Maxwell, brought to you by Dirac!

Deriving the Dirac Equation
27:28 Making things linear by getting a little complex
29:37 Hamiltonian of a free particle
30:21 Enter Pauli (σ) matrices!
31:24 Using the properties of σ matrices
35:26 Into the Matrix!
36:55 Let's add a little spin to H
41:14 The invariance of p²
43:00 Substituting H into SWE & solving
49:23 Comparison with KG equation
51:40 Conditions on α & β
53:11 {αᵢ, αⱼ} = 2 δᵢⱼ
54:10 {αᵢ, β} = 0, β² = I
54:40 What kind of matrices are α & β?
55:44 Trace of αᵢ & β
59:49 Determinants, Dimensions
1:02:00 No 4th Matrix for 2×2 :(
1:06:00 Let's try 4×4 :)
1:07:58 Tr(αᵢ), Tr(β)
1:08:43 {αᵢ, αⱼ} = 2 δᵢⱼ
1:12:00 αᵢβ + βαᵢ = 0
1:14:10 Back to the equation
1:15:33 Ψ is 4x1
1:16:04 Let β = γ⁰, βα = γ
1:17:36 THE DIRAC EQUATION
1:19:10 Properties of γ matrices

Discussion
1:23:04 Dirac handles everything beautifully
1:26:03 Up Next
1:27:39 Can't talk enough about Dirac
1:30:17 Einstein, Dirac, Feynman, more Dirac
1:34:12 Who will bring a revolution in Physics?


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