100 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
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
Exact flow equation for bound states
We develop a formalism to describe the formation of bound states in quantum
field theory using an exact renormalization group flow equation. As a concrete
example we investigate a nonrelativistic field theory with instantaneous
interaction where the flow equations can be solved exactly. However, the
formalism is more general and can be applied to relativistic field theories, as
well. We also discuss expansion schemes that can be used to find approximate
solutions of the flow equations including the essential momentum dependence.Comment: 22 pages, references added, published versio
Perturbative Tamm-Dancoff Renormalization
A new two-step renormalization procedure is proposed. In the first step, the
effects of high-energy states are considered in the conventional (Feynman)
perturbation theory. In the second step, the coupling to many-body states is
eliminated by a similarity transformation. The resultant effective Hamiltonian
contains only interactions which do not change particle number. It is subject
to numerical diagonalization. We apply the general procedure to a simple
example for the purpose of illustration.Comment: 20 pages, RevTeX, 10 figure
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.
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 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
Light-cone quantization of two dimensional field theory in the path integral approach
A quantization condition due to the boundary conditions and the
compatification of the light cone space-time coordinate is identified at
the level of the classical equations for the right-handed fermionic field in
two dimensions. A detailed analysis of the implications of the implementation
of this quantization condition at the quantum level is presented. In the case
of the Thirring model one has selection rules on the excitations as a function
of the coupling and in the case of the Schwinger model a double integer
structure of the vacuum is derived in the light-cone frame. Two different
quantized chiral Schwinger models are found, one of them without a
-vacuum structure. A generalization of the quantization condition to
theories with several fermionic fields and to higher dimensions is presented.Comment: revtex, 14 p
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