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Recently we have studied the Bloch effective Hamiltonian approach to boundstates in 2+1 dimensional gauge theories. Numerical calculations were carriedout to investigate the vanishing energy denominator problem. In this work westudy similarity renormalization approach to the same problem. By performinganalytical calculations with a step function form for the similarity factor, weshow that in addition to curing the vanishing energy denominator problem,similarity approach generates linear confining interaction for large transverseseparations. However, for large longitudinal separations, the generatedinteraction grows only as the square root of the longitudinal separation andhence produces violations of rotational symmetry in the spectrum. We carry outnumerical studies in the G{\l}azek-Wilson and Wegner formalisms and present lowlying eigenvalues and wavefunctions. We investigate the sensitivity of thespectra to various parameterizations of the similarity factor and otherparameters of the effective Hamiltonian, especially the scale $\sigma$. Ourresults illustrate the need for higher order calculations of the effectiveHamiltonian in the similarity renormalization scheme.Comment: 31 pages, 4 figures, to be published in Physical Review

physical review. d. particles, fields, gravitation, and cosmology/physical review. d. particles and fields

Mesons in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mn /><mml:mo>(</mml:mo><mml:mn>2</mml:mn><mml:mo>+</mml:mo><mml:mn>1</mml:mn><mml:mo>)</mml:mo><mml:mn /></mml:math>-dimensional light front QCD. II. Similarity renormalization approach

Mesons in(2+1)-dimensional light front QCD. II. Similarity renormalization approach