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Foundations
ADVANCED
12 units

Geometry, Topology & Group Theory for Physics

A physics-first route through manifolds, Lie groups, representations, topology, fiber bundles, gauge connections, and Berry phase.

12 units18 hoursADVANCED
Open student course

Published syllabus

Course Units

Unit 1
90 min

Manifolds as configuration spaces

Admin-authored unit for Geometry, Topology & Group Theory for Physics.

Course notes
3 objectives
Unit 2
90 min

Tangent spaces, cotangent spaces, and metrics

Admin-authored unit for Geometry, Topology & Group Theory for Physics.

Course notes
3 objectives
Unit 3
90 min

Curvature, geodesics, and parallel transport

Admin-authored unit for Geometry, Topology & Group Theory for Physics.

Course notes
3 objectives
Unit 4
90 min

Groups, actions, and symmetry

Admin-authored unit for Geometry, Topology & Group Theory for Physics.

Course notes
3 objectives
Unit 5
90 min

Lie algebras and infinitesimal generators

Admin-authored unit for Geometry, Topology & Group Theory for Physics.

Course notes
3 objectives
Unit 6
90 min

Representations of SU(2) and spin

Admin-authored unit for Geometry, Topology & Group Theory for Physics.

Course notes
3 objectives
Unit 7
90 min

SU(3), Lorentz, and Poincare symmetry

Admin-authored unit for Geometry, Topology & Group Theory for Physics.

Course notes
3 objectives
Unit 8
90 min

Homotopy, homology, and invariants

Admin-authored unit for Geometry, Topology & Group Theory for Physics.

Course notes
3 objectives
Unit 9
90 min

Fiber bundles and gauge connections

Admin-authored unit for Geometry, Topology & Group Theory for Physics.

Course notes
3 objectives
Unit 10
90 min

Gauge curvature and holonomy

Admin-authored unit for Geometry, Topology & Group Theory for Physics.

Course notes
3 objectives
Unit 11
90 min

Berry phase and Chern numbers

Admin-authored unit for Geometry, Topology & Group Theory for Physics.

Course notes
3 objectives
Unit 12
90 min

Topological defects, anomalies, and research links

Admin-authored unit for Geometry, Topology & Group Theory for Physics.

Course notes
3 objectives