Scope of questions for State exams of Master's degree program
Branch: Mathematical Physics
Subject: Advanced Geometric Methods in Physics
Subjects regarding the questions:
- 02GMF2 Geometric Methods in Physics 2
- 02LIAG Lie Algebras and Lie Groups
1. Differentiable manifold, tangent vectors, tangent space, vector field and its integral curves, commutator of vector fields, tangent map
2. Exterior differential algebra, exterior and Lie derivative, Poincaré lemma, pullback of forms
3. Fibre bundle, its construction using transition functions, tangent and cotangent bundle, phase space as cotangent fibre bundle equipped with canonical 2-form, Hopf fibration
4. Principal bundle, structure group, existence of global sections and trivializability
5. Associated vector bundles
6. Connection on principal bundle, its geometrical definition, connection form
7. Curvature form, Cartan structure equations
8. Parallel transport
9. Local connection and curvature forms as gauge fields, gauge transformation
10. Covariant derivative in associated vector bundle, minimal electromagnetic interaction, Yang-Mills field