UBC Undergraduate Research

Born-Infeld action geometries Hudoba de Badyn, Mathias


In this thesis, we present a novel way of studying noncommutative geometries in string theory based on an effective Hamiltonian given by Berenstein and Dzienkowski[1]. We work in the context of the study of two magnetic monopoles deforming a D3 brane as considered by Karczmarek and Sibilia[2]. We present numerical evidence that for surfaces defined using n-dimensional generators of the SU(2) algebra in an auxiliary Hilbert space with this effective Hamiltonian, the surface represents a set of eigenvalues for 2n-dimensional eigenvectors that demonstrate the property of splitting into two parallel n-dimensional sub-eigenvectors. We conjecture that these sub-eigenvectors can then be used to study coherent states in these noncommutative geometries based on the the fact that the annihilation operator appears in block form in the effective Hamiltonian acting on the eigenvector. Lastly, we derive a useful formula for studying the geometric rate of change of these 3-dimensional surfaces in 4 dimensions that may prove handy in preparing numerical solutions of the Nahm equation.

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