Renormalized interaction of relativistic bosons with delta function potentials

Dogan C., Turgut O. T.

JOURNAL OF MATHEMATICAL PHYSICS, cilt.51, sa.8, 2010 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 51 Sayı: 8
  • Basım Tarihi: 2010
  • Doi Numarası: 10.1063/1.3456122
  • Dergi Adı: JOURNAL OF MATHEMATICAL PHYSICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • İstanbul Üniversitesi Adresli: Evet

Özet

We study the interaction of mutually noninteracting Klein-Gordon particles with localized sources on stochastically complete Riemannian surfaces. This asymptotically free theory requires regularization and coupling constant renormalization. Renormalization is performed nonperturbatively 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. (C) 2010 American Institute of Physics. [doi: 10.1063/1.3456122]