- Access by Xinjiang University
Asymptotic freedom and bound states in Hamiltonian dynamics
Phys. Rev. D 57, 3558 – Published 15 March, 1998
DOI: https://doi.org/10.1103/PhysRevD.57.3558
Abstract
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 of order 1. The small width effective Hamiltonian is projected on a small subset of the effective basis states. The resulting small matrix is diagonalized exactly and the bound state energy of the original theory is obtained with accuracy of the order of 10% using the first three terms in the perturbative expansion of the effective Hamiltonian. We briefly describe options for improving the accuracy.
References (12)
- K. G. Wilson et al., Phys. Rev. D 49, 6720 (1994).
- St. D. Głazek and K. G. Wilson, Phys. Rev. D 48, 5863 (1993).
- St. D. Głazek and K. G. Wilson, Phys. Rev. D 49, 4214 (1994).
- E.g., see, D. E. Soper, in Lattice ’96, Proceedings of the International Symposium, St. Louis, Missouri, edited by C. Bernard et al. [Nucl. Phys. B (Proc. Suppl.) 53, 69 (1997)]; M. Göckeler et al., ibid., p. 81, and references therein.
- R. J. Perry, in Theory of Hadrons and Light-Front QCD, edited by St. D. Głazek (World Scientific, Singapore, 1995), p. 56, and references therein; M. Brisudová and R. J. Perry, Phys. Rev. D 54, 1831 (1996); M. Brisudová, R. J. Perry, and K. G. Wilson, Phys. Rev. Lett. 78, 1227 (1997).
- F. Wegner, Ann. Phys. (Leipzig) 3, 77 (1994).
- E.g., see R. Jackiw, in M. A. B. Bég Memorial Volume, edited by A. Ali and P. Hoodbhoy (World Scientific, Singapore, 1991), p. 25.
- K. G. Wilson and St. D. Głazek, in Computational Physics: Proceedings of the Ninth Physics Summer School at the Australian National University, Canberra, Australia, 1996, edited by H. J. Gardner and C. M. Savage (World Scientific, Singapore, 1996), p. 197.
- W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vettering, Numerical Recipes, The Art of Scientific Computing (Cambridge University Press, New York, 1986), p. 355.
- St. D. Głazek, “Renormalization of Hamiltonians in the Light-Front Fock Space,” hep-th/9706212.
- G. P. Lepage (private communication). For a recent review of non-perturbative QCD estimates of glueball masses, see G. West, in QCD 96, Proceedings of the Conference, Montpellier, France, 1996, edited by S. Narison [Nucl. Phys. B (Proc. Suppl.) 54A, 353 (1997)].
- R. J. Perry and K. G. Wilson, Nucl. Phys. B403, 587 (1993).