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An X class solar flare has the potential to remove our satellites from orbit, permanently deactivate our main forms of communication and bring humanity into a technology-free age. By using Geant4, it is possible to simulate several layers of the Earth's atmosphere and send a simulated solar flare and coronal mass ejection. This thesis will show the interaction of photons and protons of various energies with several kilometers of atmosphere.
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In thesis we will build up our operator theory for finite and infinite dimensional systems. We then prove that Heisenberg and Schrodinger representations are equivalent for systems with finite degrees of freedom. We will then make a case to switch to a C*-algebra formulation of quantum mechanics as we will prove that the Schrodinger and Heisenberg pictures become inadequate to full describe systems with infinitely many degrees of freedom because of inequivalent representations. This becomes important as we shift from single particle systems to quantum field theory, statistical mechanics, and many other areas of study. The goal of this thesis is to introduce these mathematical topics rigorously and prove that they are necessary for further study in particle physics.