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The relentless efforts of the physics community has not yet availed us thesolution of how to unify the Quantum Mechanics with General Relativity, apuzzle that has engaged the minds of the physicists for almost a century. Theinsufficiency of today's and foreseeable future's technology for a direct reachinto the Planck energies at which the fundamental theory, the Quantum Theory ofGravity, lies has lead to the search of the low energy effects of thatfundamental Planck level theory irregardless of the details of it. In thisthesis, one of the leading candidates of such an exotic effect, that is theviolation of Lorentz and CPT symmetries is analyzed. The action level effectivefield theoretical framework for such an analysis called Standard ModelExtension has already been in the literature for the last two decades; here,the nonminimal photon sector of such a framework is examined from a quantumfield theoretical point of view. All possible polarization vectors fordifferent kinds of CPT violations, the generic forms of the dispersionrelations that these polarization vectors satisfy, and the correspondingpropagators of the photon field are explicitly calculated. Special models ofLorentz violations are introduced, and a particular one called vacuumorthogonal model is analyzed extensively. It is found that this particular formof Lorentz violation cannot induce any effects that is detectable in the vacuumpropagation of the photon. Isotropic and leading order cases of the Lorentzviolation is studied and this found result is explicitly shown.

A Lorentz Violating Theory: Its Nonminimal Extension in the Photon Sector