Yang-Mills theory on Lorentzian four-manifolds

Goal: Understand the mathematical formulation of pure Yang-Mills
theory on a Lorentzian 4-manifold.

Group Leader: Narcisa Haiducu

Study Team: Narcisa Haiducu

Supervisor: Calin Lazaroiu

Scheme:

A. Basic theory of Lorentzian four-manifolds.

B. Basic theory of principal bundles and associated vector
bundles. The adjoint bundle of a principal bundle.

C. Theory of principal and adjoint connections.

D. The Yang-Mills action and its equations of motion on a Lorentzian
four-manifold.

E. Aplication to semisimple structure groups. The case of U(n) and
SU(n) Yang-Mills theory.

Bonus: Basic Chern-Weil theory

Historical: 50 mins presentation of the history of Yang-Mills theory and the main people who contributed to it.

References:

J. K. Beem, P. E. Ehrlich, K. L. Easley, "Global Lorentzian Geometry"

O'Neill, "Semi-Riemannian Geometry With Applications to Relativity"

M. Javaloyes, M. Sanches, "An Introduction to Lorentzian Geometry and its Applications"

Kobayashi & Nomizu, "Foundations of Differential Geometry"

L. W. Tu, "Differential Geometry: Connections, Curvature, and characteristic Classes"

Michor, "Topics in differental geometry"

Atiyah, "Geometry of Yang-Mills fields", Lecture Notes in Physics, vol. 80

Gockeler & Schucker, "Differential Geometry, Gauge Theories, and Gravity"