Asymptotic Freedom and Bound States in Hamiltonian Dynamics

Details Asymptotic Freedom and Bound States in Hamiltonian Dynamics Asymptotic Freedom and Bound States in Hamiltonian Dynamics

1997-07-02

arxiv.org/abs/hep-th/9707028v1

Phys.Rev. D57 (1998) 3558-3566

Physics

High Energy Physics

High Energy Physics - Theory

plain latex file, 15 pages, 6 latex figures 1 page each, 1 table

Scientific paper

10.1103/PhysRevD.57.3558

We study a model of asymptotically free theories with bound states using the similarity renormalization group for hamiltonians. We find that the renormalized effective hamiltonians can be approximated in a large range of widths by introducing similarity factors and the running coupling constant. This approximation loses accuracy for the small widths on the order of the bound state energy and it is improved by using the expansion in powers of the running coupling constant. The coupling constant for small widths is order 1. The small width effective hamiltonian is projected on a small subset of the effective basis states. The resulting small matrix is diagonalized and the exact bound state energy is obtained with accuracy of the order of 10% using the first three terms in the expansion. We briefly describe options for improving the accuracy.

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