Münster 2002 – scientific programme
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HK: Physik der Hadronen und Kerne
HK 9: Poster Session: Theory
HK 9.8: Poster
Tuesday, March 12, 2002, 10:30–12:45, Foyer Chemie
Study of relativistic bound states in a scalar model using diagonalization/Monte Carlo methods — •Buḡra Borasoy1 and Dean Lee2 — 1Physik Department, Technische Universität München — 2North Carolina State University, Raleigh, USA
A recently proposed diagonalization/Monte Carlo computational scheme is used to study relativistic two-body and three-body bound states in (φ6− φ 4)1+1 theory. Diagonalization makes it possible to extract detailed information about wavefunctions and excited states, while Monte Carlo allows one to handle the exponential increase in the number of basis states for large volume systems. The first half of the method involves finding and diagonalizing the Hamiltonian restricted to an optimal subspace which includes the most important basis vectors of the lowest energy eigenstates. Once the most important basis vectors are found and their interactions treated exactly, Monte Carlo is used to sample the contribution of the remaining basis vectors. In this investigation we demonstrate how the new diagonalization/Monte Carlo scheme is applied to the study of relativistic bound states which are of primary interest to particle and nuclear physics. We also derive solutions to the non-relativistic versions of the two- body and three-body bound state problems and compare our numerical results for the relativistic bound states energies and wavefunctions with an assortment of different approximations and results from the literature. We find that the approach is well-suited for calculating bound state energies and wavefunctions.
Work supported in part by the DFG.