2019/07/28 by Yesukhei Jagvaral, Jagvaral, Yesukhei, O. Teoman Turgut +3
Mathematics · Physics and Astronomy · #81Q10 #81Q70 #Advanced Operator Algebra Research #Cold Atom Physics and Bose-Einstein Condensates #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.1907.12102
openalex publication_date 2019/07/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We reexamine the relativistic 2+1 dimensional Lee model in light-front coordinates on flat space and on a space-time with a spatial section given by a compact manifold in the usual canonical formalism. The simpler 2+1 dimension is chosen because renormalization is needed only for the mass difference but not required for the coupling constant and the wavefunction. The model is constructed non-perturbatively based on the resolvent formulation [1]. The bound state spectrum is studied through its ``principal operator" and bounds for the ground state energy are obtained. We show that the formal expression found indeed defines the resolvent of a self-adjoint operator--the Hamiltonian of the interacting system. Moreover, we prove an essential result that the principal operator corresponds to a self-adjoint holomorphic family of type-A in the sense of Kato.