Lee model and its resolvent analysis
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We revisit the relativistic (2+1)-dimensional Lee model on flat space in light-front coordinates 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 wave function. The model is constructed non-perturbatively based on the resolvent formulation [B. T. Kaynak and O. T. Turgut, The relativistic Lee model on Riemannian manifolds, J. Phys. A: Math. Theor. 42(22) (2009) 225402]. 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.
Originalsprog | Engelsk |
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Artikelnummer | 2350055 |
Tidsskrift | International Journal of Geometric Methods in Modern Physics |
Vol/bind | 20 |
Udgave nummer | 4 |
Antal sider | 35 |
ISSN | 0219-8878 |
DOI | |
Status | Udgivet - 2023 |
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