Singular interactions supported by embedded curves

Abstract

In this work, singular interactions supported by embedded curves on Riemannian manifolds are discussed from a more direct and physical perspective, via the heat kernel approach. We show that the renormalized problem is well defined, the ground state is finite and the corresponding wavefunction is positive. The renormalization group invariance of the model is also discussed.

Published version, 15 pages, no figures. arXiv admin note: substantial text overlap with arXiv:1204.1853

References in corpus (2)

• Leaky Quantum Graphs: A Review
• Point Interaction in two and three dimensional Riemannian Manifolds

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• Recursion formula for the Green's function of a Hamiltonian for several types of Dirac delta-function potentials in curved spaces
• Infinitely many singular interactions on noncompact manifolds