Professor Tonnis ter Veldhuis provides Macalester students with research opportunities in theoretical physics. In the Summer of 2020, a team of three students were introduced to the method of nonlinear realization of symmetries by studying Prof. Veldhuis’s prior research regarding an application of the method to membrane dynamics (1). Subsequent developments of this prior work involved research into torsion and riemann curvature tensors, as well as metric compatibility, highlighting the connection between symmetry and space-time structure. The foundation of this work was the D=4 Poincare algebra in the D=3 Lorentz group covariant form. After this introduction, each team member developed their own individual project. For my own original research, I began by constructing the D=4 Maxwell algebra, and obtained an invariant action corresponding to the dynamics of a charged particle in an external electromagnetic field through application of the same method of nonlinear realizations that I was introduced to earlier in the program. Further developments of my research involved a super-symmetrization of the Maxwell algebra, as well as an attempt to retrieve the action corresponding to spinning charged particles.

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