Interaction of Relativistic Bosons with Localized Sources on Riemannian Surfaces

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.

29 pages

References in corpus (3)

• Finitely Many Dirac-Delta Interactions on Riemannian Manifolds
• Relativistic Lee Model on Riemannian Manifolds
• Nonrelativistic Lee model in three dimensional Riemannian manifolds

Cited by in corpus (7)

• One-Dimensional Semirelativistic Hamiltonian with Multiple Dirac Delta Potentials
• Existence of Hamiltonians for Some Singular Interactions on Manifolds
• On the Number of Bound States of Point Interactions on Hyperbolic Manifolds
• Non-relativistic Lee Model on two Dimensional Riemannian Manifolds
• A Perturbative Approach to the Tunneling Phenomena
• A Klein Gordon Particle Captured by Embedded Curves
• On Schrödinger Operators Modified by $\delta$ Interactions