2001/10/17 by Dipankar Chakrabarti, A. Harindranath
Physics and Astronomy · #Computer science #Database #High-Energy Particle Collisions Research #Particle physics theoretical and experimental studies #Quantum Chromodynamics and Particle Interactions #hep-th
paper · pdf · doi:10.1103/physrevd.65.045001
published as Phys.Rev. D65 (2002) 045001 · 31 pages, 4 figures, to be published in Physical Review D
arxiv created 2001/10/17 · openalex publication_date 2002/01/14 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
Recently, we have studied the Bloch effective Hamiltonian approach to bound states in (2+1)-dimensional gauge theories. Numerical calculations were carried out to investigate the vanishing energy denominator problem. In this work, we study a similarity renormalization approach to the same problem. By performing analytical calculations with a step function form for the similarity factor, we show that, in addition to curing the vanishing energy denominator problem, the similarity approach generates a linear confining interaction for large transverse separations. However, for large longitudinal separations, the generated interaction grows only as the square root of the longitudinal separation and hence produces violations of rotational symmetry in the spectrum. We carry out numerical studies in the G\lazek-Wilson and Wegner formalisms and present low-lying eigenvalues and wave functions. We investigate the sensitivity of the spectra to various parametrizations of the similarity factor and other parameters of the effective Hamiltonian, especially the scale \ensuremathσ. Our results illustrate the need for higher-order calculations of the effective Hamiltonian in the similarity renormalization scheme.