TY - JOUR

T1 - Lee model and its resolvent analysis

AU - Jagvaral, Yesukhei

AU - Turgut, O. Teoman

AU - Ünel, Meltem

N1 - Publisher Copyright: © 2023 World Scientific Publishing Company.

PY - 2023

Y1 - 2023

N2 - 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.

AB - 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.

KW - Exact Renormalization

KW - fields in background metric

KW - heat kernel methods

KW - holomorphic family of operators

KW - light-front quantization

KW - operator methods in quantum fields

KW - self-adjoint operators in quantum theory

KW - Wigner-Weiskopf model

UR - http://www.scopus.com/inward/record.url?scp=85144525719&partnerID=8YFLogxK

U2 - 10.1142/S021988782350055X

DO - 10.1142/S021988782350055X

M3 - Journal article

AN - SCOPUS:85144525719

VL - 20

JO - International Journal of Geometric Methods in Modern Physics

JF - International Journal of Geometric Methods in Modern Physics

SN - 0219-8878

IS - 4

M1 - 2350055

ER -