73 research outputs found
21st Century Ergonomic Education, From Little e to Big E
Despite intense efforts, contemporary educational systems are not enabling
individuals to function optimally in modern society. The main reason is that
reformers are trying to improve systems that are not designed to take advantage
of the centuries of history of the development of today's societies. Nor do
they recognize the implications of the millions of years of history of life on
earth in which humans are the latest edition of learning organisms. The
contemporary educational paradigm of "education for all" is based on a 17th
century model of "printing minds" for passing on static knowledge. This
characterizes most of K-12 education. In contrast, 21st Century education
demands a new paradigm, which we call Ergonomic Education. This is an education
system that is designed to fit the students of any age instead of forcing the
students to fit the education system. It takes into account in a fundamental
way what students want to learn -- the concept "wanting to learn" refers to the
innate ability and desire to learn that is characteristic of humans. The
Ergonomic Education paradigm shifts to education based on coaching students as
human beings who are hungry for productive learning throughout their lives from
their very earliest days.Comment: plain latex, 13 pages, 1 tabl
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
Renormalization of Schr\"odinger Equation and Wave Functional for Rapidly Oscillating Fields in QCD
Background field method is used to perform renormalization group
transformations for Schr\"odinger equation in QCD. The dependence of the ground
state wave functional on rapidly oscillating fields is found.Comment: 8pp., Late
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
Nonperturbative renormalization in a scalar model within Light-Front Dynamics
Within the covariant formulation of Light-Front Dynamics, in a scalar model
with the interaction Hamiltonian , we calculate
nonperturbatively the renormalized state vector of a scalar "nucleon" in a
truncated Fock space containing the , and sectors. The
model gives a simple example of non-perturbative renormalization which is
carried out numerically. Though the mass renormalization diverges
logarithmically with the cutoff , the Fock components of the "physical"
nucleon are stable when .Comment: 22 pages, 5 figure
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
Pseudo-nearrings and quasi-modules over them
In this paper we start to investigate a new notion of pseudo-nearrings and a generalization of linear spaces to quasi-modules over pseudo-nearrings. Pseudo-nearrings can be treated as ringoids in the sense of J. Hion (see [6]). The idea of pseudo-nearings is based on the notion of a ∗-associative quasigroup, i.e. on an involutive groupoid (A;+,* ) in which the following identities hold: (x*)* = x, (x + y)* = y* + x*, (x + y)* + z = x + (y + z)*. We assume also commutativity and quasigroup properties of (A;+)
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
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
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
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