224 research outputs found
Spin in relativistic quantum theory
We discuss the role of spin in Poincar\'e invariant formulations of quantum
mechanics.Comment: 54 page
Comparison of Relativistic Nucleon-Nucleon Interactions
We investigate the difference between those relativistic models based on
interpreting a realistic nucleon-nucleon interaction as a perturbation of the
square of a relativistic mass operator and those models that use the method of
Kamada and Gl\"ockle to construct an equivalent interaction to add to the
relativistic mass operator. Although both models reproduce the phase shifts and
binding energy of the corresponding non-relativistic model, they are not
scattering equivalent. The example of elastic electron-deuteron scattering in
the one-photon-exchange approximation is used to study the sensitivity of
three-body observables to these choices. Our conclusion is that the differences
in the predictions of the two models can be understood in terms of the
different ways in which the relativistic and non-relativistic -matrices are
related. We argue that the mass squared method is consistent with conventional
procedures used to fit the Lorentz-invariant cross section as a function of the
laboratory energy.Comment: Revtex 13 pages, 5 figures, corrected some typo
Vacuum Structures in Hamiltonian Light-Front Dynamics
Hamiltonian light-front dynamics of quantum fields may provide a useful
approach to systematic non-perturbative approximations to quantum field
theories. We investigate inequivalent Hilbert-space representations of the
light-front field algebra in which the stability group of the light-front is
implemented by unitary transformations. The Hilbert space representation of
states is generated by the operator algebra from the vacuum state. There is a
large class of vacuum states besides the Fock vacuum which meet all the
invariance requirements. The light-front Hamiltonian must annihilate the vacuum
and have a positive spectrum. We exhibit relations of the Hamiltonian to the
nontrivial vacuum structure.Comment: 16 pages, report \# ANL-PHY-7524-TH-93, (Latex
Quantitative Relativistic Effects in the Three-Nucleon Problem
The quantitative impact of the requirement of relativistic invariance in the
three-nucleon problem is examined within the framework of Poincar\'e invariant
quantum mechanics. In the case of the bound state, and for a wide variety of
model implementations and reasonable interactions, most of the quantitative
effects come from kinematic factors that can easily be incorporated within a
non-relativistic momentum-space three-body code.Comment: 15 pages, 15 figure
A light-front coupled cluster method
A new method for the nonperturbative solution of quantum field theories is
described. The method adapts the exponential-operator technique of the standard
many-body coupled-cluster method to the Fock-space eigenvalue problem for
light-front Hamiltonians. This leads to an effective eigenvalue problem in the
valence Fock sector and a set of nonlinear integral equations for the functions
that define the exponential operator. The approach avoids at least some of the
difficulties associated with the Fock-space truncation usually used.Comment: 8 pages, 1 figure; to appear in the proceedings of LIGHTCONE 2011,
23-27 May 2011, Dalla
Wavelet Methods in the Relativistic Three-Body Problem
In this paper we discuss the use of wavelet bases to solve the relativistic
three-body problem. Wavelet bases can be used to transform momentum-space
scattering integral equations into an approximate system of linear equations
with a sparse matrix. This has the potential to reduce the size of realistic
three-body calculations with minimal loss of accuracy. The wavelet method leads
to a clean, interaction independent treatment of the scattering singularities
which does not require any subtractions.Comment: 14 pages, 3 figures, corrected referenc
Ground state correlations and mean-field in O: Part II
We continue the investigations of the O ground state using the
coupled-cluster expansion [] method with realistic nuclear
interaction. In this stage of the project, we take into account the three
nucleon interaction, and examine in some detail the definition of the internal
Hamiltonian, thus trying to correct for the center-of-mass motion. We show that
this may result in a better separation of the internal and center-of-mass
degrees of freedom in the many-body nuclear wave function. The resulting ground
state wave function is used to calculate the "theoretical" charge form factor
and charge density. Using the "theoretical" charge density, we generate the
charge form factor in the DWBA picture, which is then compared with the
available experimental data. The longitudinal response function in inclusive
electron scattering for O is also computed.Comment: 9 pages, 7 figure
Vector mesons in a relativistic point-form approach
We apply the point form of relativistic quantum mechanics to develop a
Poincare invariant coupled-channel formalism for two-particle systems
interacting via one-particle exchange. This approach takes the exchange
particle explicitly into account and leads to a generalized eigenvalue equation
for the Bakamjian-Thomas type mass operator of the system. The coupling of the
exchange particle is derived from quantum field theory. As an illustrative
example we consider vector mesons within the chiral constituent quark model in
which the hyperfine interaction between the confined quark-antiquark pair is
generated by Goldstone-boson exchange. We study the effect of retardation in
the Goldstone-boson exchange by comparing with the commonly used instantaneous
approximation. As a nice physical feature we find that the problem of a too
large - splitting can nearly be avoided by taking the dynamics of
the exchange meson explicitly into account.Comment: 14 pages, 1 figur
Gauge-invariant theory of pion photoproduction with dressed hadrons
Based on an effective field theory of hadrons in which quantum chromodynamics
is assumed to provide the necessary bare cutoff functions, a gauge-invariant
theory of pion photoproduction with fully dressed nucleons is developed. The
formalism provides consistent dynamical descriptions of pi-N --> pi-N
scattering and Gamma-N --> pi-N production mechanisms in terms of nonlinear
integral equations for fully dressed hadrons. Defining electromagnetic currents
via the gauging of hadronic n-point Green's functions, dynamically detailed
currents for dressed nucleons are introduced. The dressed hadron currents and
the pion photoproduction current are explicitly shown to satisfy gauge
invariance in a self-consistent manner. Approximations are discussed that make
the nonlinear formalism manageable in practice and yet preserve gauge
invariance. This is achieved by recasting the gauge conditions for all
contributing interaction currents as continuity equations with ``surface''
terms for the individual particle legs coming into or going out of the hadronic
interaction region. General procedures are given that approximate any type of
(global) interaction current in a gauge-invariance preserving manner as a sum
of single-particle ``surface'' currents. It is argued that these prescriptions
carry over to other reactions, irrespective of the number or type of
contributing hadrons or hadronic systems.Comment: 33 pages, RevTeX; includes 8 postscript figures (requires psfig.sty).
This version corrects some minor errors, etc.; contains updated references.
Accepted for publication in Phys. Rev. C56 (Oct. 97
First Order Relativistic Three-Body Scattering
Relativistic Faddeev equations for three-body scattering at arbitrary
energies are formulated in momentum space and in first order in the two-body
transition-operator directly solved in terms of momentum vectors without
employing a partial wave decomposition. Relativistic invariance is incorporated
within the framework of Poincare invariant quantum mechanics, and presented in
some detail.
Based on a Malfliet-Tjon type interaction, observables for elastic and
break-up scattering are calculated up to projectile energies of 1 GeV. The
influence of kinematic and dynamic relativistic effects on those observables is
systematically studied. Approximations to the two-body interaction embedded in
the three-particle space are compared to the exact treatment.Comment: 26 pages, 13 figure
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