### Interaction of Relativistic Bosons with Localized Sources on Riemannian SurfacesInteraction of Relativistic Bosons with Localized Sources on Riemannian Surfaces

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 Author Doğan, Çağlar ♦ Turgut, O. Teoman Source arXiv.org Content type Text File Format PDF Date of Submission 2009-12-02 Language English
 Subject Domain (in DDC) Computer science, information & general works ♦ Natural sciences & mathematics ♦ Physics Subject Keyword High Energy Physics - Theory ♦ physics:hep-th Abstract We study the interaction of mutually non-interacting Klein-Gordon particles with localized sources on stochastically complete Riemannian surfaces. This asymptotically free theory requires regularization and coupling constant renormalization. Renormalization is performed non-perturbatively using the orthofermion algebra technique and the principal operator $\Phi$ is found. The principal operator is then used to obtain the bound state spectrum, in terms of binding energies to single Dirac-delta function centers. The heat kernel method allows us to generalize this procedure to compact and Cartan-Hadamard type Riemannian manifolds. We make use of upper and lower bounds on the heat kernel to constrain the ground state energy from below thus confirming that our neglect of pair creation is justified for certain ranges of parameters in the problem. Educational Use Research Learning Resource Type Article Page Count 29