Lie Groups, Manifolds, Gauge Fields, and Yang-Mills Equations 


By Matthew O’Cadiz

Faculty mentor: Dr. Yuan-Jen Chiang

10:00-10:50am, HCC 329

We begin by amalgamating Differential Geometry and Group theory and discuss the importance of symmetry in Mathematical Physics.  Moreover, we generalize differentiation in the tangent space of a Manifold into the Connection of the Vector Bundle of tangent spaces.  We then discuss the Gauge Transformations between two bundles of the tangent space of a manifold locally.  We finally derive Yang-Mills equations based on Connections, Tangent Bundles, and Gauge Fields, by Euler Lagrange equation. 


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