67,575 research outputs found
Systematic Renormalization in Hamiltonian Light-Front Field Theory
We develop a systematic method for computing a renormalized light-front field
theory Hamiltonian that can lead to bound states that rapidly converge in an
expansion in free-particle Fock-space sectors. To accomplish this without
dropping any Fock sectors from the theory, and to regulate the Hamiltonian, we
suppress the matrix elements of the Hamiltonian between free-particle
Fock-space states that differ in free mass by more than a cutoff. The cutoff
violates a number of physical principles of the theory, and thus the
Hamiltonian is not just the canonical Hamiltonian with masses and couplings
redefined by renormalization. Instead, the Hamiltonian must be allowed to
contain all operators that are consistent with the unviolated physical
principles of the theory. We show that if we require the Hamiltonian to produce
cutoff-independent physical quantities and we require it to respect the
unviolated physical principles of the theory, then its matrix elements are
uniquely determined in terms of the fundamental parameters of the theory. This
method is designed to be applied to QCD, but for simplicity, we illustrate our
method by computing and analyzing second- and third-order matrix elements of
the Hamiltonian in massless phi-cubed theory in six dimensions.Comment: 47 pages, 6 figures; improved referencing, minor presentation change
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
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
Similarity Renormalization, Hamiltonian Flow Equations, and Dyson's Intermediate Representation
A general framework is presented for the renormalization of Hamiltonians via
a similarity transformation. Divergences in the similarity flow equations may
be handled with dimensional regularization in this approach, and the resulting
effective Hamiltonian is finite since states well-separated in energy are
uncoupled. Specific schemes developed several years ago by Glazek and Wilson
and contemporaneously by Wegner correspond to particular choices within this
framework, and the relative merits of such choices are discussed from this
vantage point. It is shown that a scheme for the transformation of Hamiltonians
introduced by Dyson in the early 1950's also corresponds to a particular choice
within the similarity renormalization framework, and it is argued that Dyson's
scheme is preferable to the others for ease of computation. As an example, it
is shown how a logarithmically confining potential arises simply at second
order in light-front QCD within Dyson's scheme, a result found previously for
other similarity renormalization schemes. Steps toward higher order and
nonperturbative calculations are outlined. In particular, a set of equations
analogous to Dyson-Schwinger equations is developed.Comment: REVTex, 32 pages, 7 figures (corrected references
Heavy Quark Potential from Gauge/Gravity Duality: A Large D Analysis
The heavy-quark potential is calculated in the framework of gauge/gravity
duality using the large-D approximation, where D is the number of dimensions
transverse to the flux tube connecting a quark and an antiquark in a flat
D+2-dimensional spacetime. We find that in the large-D limit the leading
correction to the ground-state energy, as given by an effective Nambu-Goto
string, arises not from the heavy modes but from the behavior of the massless
modes in the vicinity of the quark and the antiquark. We estimate this
correction and find that it should be visible in the near-future lattice QCD
calculations of the heavy-quark potential.Comment: 22 pages, 5 Figures. v2: references added, typos corrected and, Sec.
4 rewritten with an expanded non-perturbative discussion of the corrections
to the Arvis potential arising from the massless modes near the boundary of
the qcd strin
Systematic Renormalization in Hamiltonian Light-Front Field Theory: The Massive Generalization
Hamiltonian light-front field theory can be used to solve for hadron states
in QCD. To this end, a method has been developed for systematic renormalization
of Hamiltonian light-front field theories, with the hope of applying the method
to QCD. It assumed massless particles, so its immediate application to QCD is
limited to gluon states or states where quark masses can be neglected. This
paper builds on the previous work by including particle masses
non-perturbatively, which is necessary for a full treatment of QCD. We show
that several subtle new issues are encountered when including masses
non-perturbatively. The method with masses is algebraically and conceptually
more difficult; however, we focus on how the methods differ. We demonstrate the
method using massive phi^3 theory in 5+1 dimensions, which has important
similarities to QCD.Comment: 7 pages, 2 figures. Corrected error in Eq. (11), v3: Added extra
disclaimer after Eq. (2), and some clarification at end of Sec. 3.3. Final
published versio
An optical model description of momentum transfer in heavy ion collisions
An optical model description of momentum transfer in relativistic heavy ion collisions, based upon composite particle multiple scattering theory, is presented. The imaginary component of the complex momentum transfer, which comes from the absorptive part of the optical potential, is identified as the longitudinal momentum downshift of the projectile. Predictions of fragment momentum distribution observables are made and compared with experimental data. Use of the model as a tool for estimating collision impact parameters is discussed
The fractal structure of the universe : a new field theory approach
While the universe becomes more and more homogeneous at large scales,
statistical analysis of galaxy catalogs have revealed a fractal structure at
small-scales (\lambda < 100 h^{-1} Mpc), with a fractal dimension D=1.5-2
(Sylos Labini et al 1996). We study the thermodynamics of a self-gravitating
system with the theory of critical phenomena and finite-size scaling and show
that gravity provides a dynamical mechanism to produce this fractal structure.
We develop a field theoretical approach to compute the galaxy distribution,
assuming them to be in quasi-isothermal equilibrium. Only a limited, (although
large), range of scales is involved, between a short-distance cut-off below
which other physics intervene, and a large-distance cut-off, where the thermo-
dynamic equilibrium is not satisfied. The galaxy ensemble can be considered at
critical conditions, with large density fluctuations developping at any scale.
From the theory of critical phenomena, we derive the two independent critical
exponents nu and eta and predict the fractal dimension D = 1/nu to be either
1.585 or 2, depending on whether the long-range behaviour is governed by the
Ising or the mean field fixed points, respectively. Both set of values are
compatible with present observations. In addition, we predict the scaling
behaviour of the gravitational potential to be r^{-(1 + eta)/2}. That is,
r^{-0.5} for mean field or r^{- 0.519} for the Ising fixed point. The theory
allows to compute the three and higher density correlators without any
assumption or Ansatz. We find that the N-points density scales as
r_1^{(N-1)(D-3)}, when r_1 >> r_i, 2 leq i leq N . There are no free parameters
in this theory.Comment: Latex, 20 pages, no figures, to be published in the Astrophysical
Journa
Nonlinear atom-optical delta-kicked harmonic oscillator using a Bose-Einstein condensate
We experimentally investigate the atom-optical delta-kicked harmonic
oscillator for the case of nonlinearity due to collisional interactions present
in a Bose-Einstein condensate. A Bose condensate of rubidium atoms tightly
confined in a static harmonic magnetic trap is exposed to a one-dimensional
optical standing-wave potential that is pulsed on periodically. We focus on the
quantum anti-resonance case for which the classical periodic behavior is simple
and well understood. We show that after a small number of kicks the dynamics is
dominated by dephasing of matter wave interference due to the finite width of
the condensate's initial momentum distribution. In addition, we demonstrate
that the nonlinear mean-field interaction in a typical harmonically confined
Bose condensate is not sufficient to give rise to chaotic behavior.Comment: 4 pages, 3 figure
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