57 research outputs found
Small x divergences in the Similarity RG approach to LF QCD
We study small x divergences in boost invariant similarity renormalization
group approach to light-front QCD in a heavy quark-antiquark state. With the
boost invariance maintained, the infrared divergences do not cancel out in the
physical states, contrary to previous studies where boost invariance was
violated by a choice of a renormalization scale. This may be an indication that
the zero mode, or nontrivial light-cone vacuum structure, might be important
for recovering full Lorentz invariance.Comment: 23 pgs, 1 fig. Revised for publication: typos corrected, improved
discussion of regularizatio
A Density Matrix Renormalization Group Approach to an Asymptotically Free Model with Bound States
We apply the DMRG method to the 2 dimensional delta function potential which
is a simple quantum mechanical model with asymptotic freedom and formation of
bound states. The system block and the environment block of the DMRG contain
the low energy and high energy degrees of freedom, respectively. The ground
state energy and the lowest excited states are obtained with very high
accuracy. We compare the DMRG method with the Similarity RG method and propose
its generalization to field theoretical models in high energy physics.Comment: REVTEX file, 4 pages, 1 Table, 3 eps Figures. Explanation on the
extension to many-body QFT problems added, 3 new references and some minor
changes. New forma
Renormalization of Tamm-Dancoff Integral Equations
During the last few years, interest has arisen in using light-front
Tamm-Dancoff field theory to describe relativistic bound states for theories
such as QCD. Unfortunately, difficult renormalization problems stand in the
way. We introduce a general, non-perturbative approach to renormalization that
is well suited for the ultraviolet and, presumably, the infrared divergences
found in these systems. We reexpress the renormalization problem in terms of a
set of coupled inhomogeneous integral equations, the ``counterterm equation.''
The solution of this equation provides a kernel for the Tamm-Dancoff integral
equations which generates states that are independent of any cutoffs. We also
introduce a Rayleigh-Ritz approach to numerical solution of the counterterm
equation. Using our approach to renormalization, we examine several ultraviolet
divergent models. Finally, we use the Rayleigh-Ritz approach to find the
counterterms in terms of allowed operators of a theory.Comment: 19 pages, OHSTPY-HEP-T-92-01
Mesons in (2+1) Dimensional Light Front QCD. II. Similarity Renormalization Approach
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 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,
similarity approach generates 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{\l}azek-Wilson and Wegner formalisms and present low
lying eigenvalues and wavefunctions. We investigate the sensitivity of the
spectra to various parameterizations of the similarity factor and other
parameters of the effective Hamiltonian, especially the scale . Our
results illustrate the need for higher order calculations of the effective
Hamiltonian in the similarity renormalization scheme.Comment: 31 pages, 4 figures, to be published in Physical Review
Flow equations for QED in the light front dynamics
The method of flow equations is applied to QED on the light front. Requiring
that the partical number conserving terms in the Hamiltonian are considered to
be diagonal and the other terms off-diagonal an effective Hamiltonian is
obtained which reduces the positronium problem to a two-particle problem, since
the particle number violating contributions are eliminated. No infrared
divergencies appear. The ultraviolet renormalization can be performed
simultaneously.Comment: 15 pages, Latex, 3 pictures, Submitted to Phys.Rev.
Non-perturbative flow equations from continuous unitary transformations
We use a novel parameterization of the flowing Hamiltonian to show that the
flow equations based on continuous unitary transformations, as proposed by
Wegner, can be implemented through a nonlinear partial differential equation
involving one flow parameter and two system specific auxiliary variables. The
implementation is non-perturbative as the partial differential equation
involves a systematic expansion in fluctuations, controlled by the size of the
system, rather than the coupling constant. The method is applied to the Lipkin
model to construct a mapping which maps the non-interacting spectrum onto the
interacting spectrum to a very high accuracy. This function is universal in the
sense that the full spectrum for any (large) number of particles can be
obtained from it. In a similar way expectation values for a large class of
operators can be obtained, which also makes it possible to probe the stucture
of the eigenstates.Comment: 24 pages, 13 figure
Associative polynomial functions over bounded distributive lattices
The associativity property, usually defined for binary functions, can be
generalized to functions of a given fixed arity n>=1 as well as to functions of
multiple arities. In this paper, we investigate these two generalizations in
the case of polynomial functions over bounded distributive lattices and present
explicit descriptions of the corresponding associative functions. We also show
that, in this case, both generalizations of associativity are essentially the
same.Comment: Final versio
Glueballs in a Hamiltonian Light-Front Approach to Pure-Glue QCD
We calculate a renormalized Hamiltonian for pure-glue QCD and diagonalize it.
The renormalization procedure is designed to produce a Hamiltonian that will
yield physical states that rapidly converge in an expansion in free-particle
Fock-space sectors. To make this possible, we use light-front field theory to
isolate vacuum effects, and we place a smooth cutoff on the Hamiltonian to
force its free-state matrix elements to quickly decrease as the difference of
the free masses of the states increases. The cutoff violates a number of
physical principles of light-front pure-glue QCD, including Lorentz covariance
and gauge covariance. This means that the operators in the Hamiltonian are not
required to respect these physical principles. However, by requiring the
Hamiltonian to produce cutoff-independent physical quantities and by requiring
it to respect the unviolated physical principles of pure-glue QCD, we are able
to derive recursion relations that define the Hamiltonian to all orders in
perturbation theory in terms of the running coupling. We approximate all
physical states as two-gluon states, and use our recursion relations to
calculate to second order the part of the Hamiltonian that is required to
compute the spectrum. We diagonalize the Hamiltonian using basis-function
expansions for the gluons' color, spin, and momentum degrees of freedom. We
examine the sensitivity of our results to the cutoff and use them to analyze
the nonperturbative scale dependence of the coupling. We investigate the effect
of the dynamical rotational symmetry of light-front field theory on the
rotational degeneracies of the spectrum and compare the spectrum to recent
lattice results. Finally, we examine our wave functions and analyze the various
sources of error in our calculation.Comment: 75 pages, 17 figures, 1 tabl
Flow equations for Hamiltonians: Contrasting different approaches by using a numerically solvable model
To contrast different generators for flow equations for Hamiltonians and to
discuss the dependence of physical quantities on unitarily equivalent, but
effectively different initial Hamiltonians, a numerically solvable model is
considered which is structurally similar to impurity models. By this we discuss
the question of optimization for the first time. A general truncation scheme is
established that produces good results for the Hamiltonian flow as well as for
the operator flow. Nevertheless, it is also pointed out that a systematic and
feasible scheme for the operator flow on the operator level is missing. For
this, an explicit analysis of the operator flow is given for the first time. We
observe that truncation of the series of the observable flow after the linear
or bilinear terms does not yield satisfactory results for the entire parameter
regime as - especially close to resonances - even high orders of the exact
series expansion carry considerable weight.Comment: 25 pages, 10 figure
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