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Group Theory for Physics
The mathematics of symmetry — from the four group axioms to the SU(3)×SU(2)×U(1) structure of the Standard Model. Essential for quantum mechanics, particle physics, and beyond.
1
What is a Group?
The four axioms that define a group, with examples from number theory and geometry.
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2
Subgroups & Lagrange's Theorem
How groups contain smaller groups, and why subgroup order must divide group order.
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3
Homomorphisms & Isomorphisms
Structure-preserving maps between groups, the first isomorphism theorem, and when two groups are the same.
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4
Representation Theory
How groups act on vector spaces — the bridge from abstract algebra to quantum mechanics.
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5
Lie Groups
Continuous symmetry groups with smooth structure — from rotations to gauge transformations.
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6
Lie Algebras
Infinitesimal generators, commutation relations, and the structure constants that classify all symmetries.
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7
SU(2) and Angular Momentum
Pauli matrices, spin representations, and the deep reason angular momentum is quantized.
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8
SU(3) and the Standard Model
The eight Gell-Mann matrices, color charge, quark multiplets, and the gauge structure of the strong force.
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