101 research outputs found
Similarity Renormalization Group for Few-Body Systems
Internucleon interactions evolved via flow equations yield soft potentials
that lead to rapid variational convergence in few-body systems.Comment: 3 pages, 6 figures. To appear in the proceedings of the 20th European
Conference on Few-Body Problems in Physics (EFB20), Pisa, September 10-14,
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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
Ridge Production in High-Multiplicity Hadronic Ultra-Peripheral Proton-Proton Collisions
An unexpected result at the RHIC and the LHC is the observation that
high-multiplicity hadronic events in heavy-ion and proton-proton collisions are
distributed as two "ridges", approximately flat in rapidity and opposite in
azimuthal angle. We propose that the origin of these events is due to the
inelastic collisions of aligned gluonic flux tubes that underly the color
confinement of the quarks in each proton. We predict that high-multiplicity
hadronic ridges will also be produced in the high energy photon-photon
collisions accessible at the LHC in ultra-peripheral proton-proton collisions
or at a high energy electron-positron collider. We also note the orientation of
the flux tubes between the quark and antiquark of each high energy photon will
be correlated with the plane of the scattered proton or lepton. Thus hadron
production and ridge formation can be controlled in a novel way at the LHC by
observing the azimuthal correlations of the scattering planes of the
ultra-peripheral protons with the orientation of the produced ridges.
Photon-photon collisions can thus illuminate the fundamental physics underlying
the ridge effect and the physics of color confinement in QCD.Comment: Presented by SJB at Photon 2017: The International Conference on the
Structure and the Interactions of the Photon and the International Workshop
on Photon-Photon Collisions. CERN, May 22-26, 2017. References adde
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
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
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
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
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
Relativistic bound states in Yukawa model
The bound state solutions of two fermions interacting by a scalar exchange
are obtained in the framework of the explicitly covariant light-front dynamics.
The stability with respect to cutoff of the J= and J=
states is studied. The solutions for J= are found to be stable for
coupling constants below the critical value
and unstable above it. The asymptotic behavior of the
wave functions is found to follow a law. The coefficient
and the critical coupling constant are calculated from an
eigenvalue equation. The binding energies for the J= solutions
diverge logarithmically with the cutoff for any value of the coupling constant.
For a wide range of cutoff, the states with different angular momentum
projections are weakly split.Comment: 22 pages, 13 figures, .tar.gz fil
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