Applying the Non-Relavistic Standard Model Extension to Hydrogen
Yoder, Theodore J.
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During its 40 year lifetime, the standard model of particle physics has come to be well established experimentally. However, straightforward extensions of the standard model can be valuable guides for observations of potentially non-standard phenomena. The standard model extension (SME) naturally generalizes the standard model to include Lorentz and CPT violation. A number of new terms in the SME Lagrangian serve to incorporate these symmetry violations in a renormalizable e ective eld theory. Each term is controlled in magnitude by an SME tensor, which is a parameter in the theory. Determining these parameters, which so far are believed to be nearly if not exactly zero, is the object of experimental searches for Lorentz or CPT violation that use the SME as a guide. Our ultimate goal in this work is the calculation of the SME corrections to the free hydrogen energy levels through order SME 2. Starting from the extended Dirac equation, we nd the non-relativistic SME Hamiltonian for fermions to rst order in the SME parameters and second order in momentum using the standard Foldy-Wouthuysen procedure. The SME Hamiltonian is that of the SM, augmented by additive terms involving the SME parameters. We performed a perturbative calculation with the SME-extended, non-relativistic e ective hamiltonian to nd the modi ed energy levels of hydrogen. This calculation was carried out for all eigenstates of total angular momentum in free hydrogen.
Franklin and Marshall College Archives, Undergraduate Honors Thesis 2012
- F&M Theses Collection 
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