44 research outputs found
Perturbation theory in light-cone quantization
A thorough investigation of light-cone properties which are characteristic for higher dimensions is very important. The easiest way of addressing these issues is by analyzing the perturbative structure of light-cone field theories first. Perturbative studies cannot be substituted for an analysis of problems related to a nonperturbative approach. However, in order to lay down groundwork for upcoming nonperturbative studies, it is indispensable to validate the renormalization methods at the perturbative level, i.e., to gain control over the perturbative treatment first. A clear understanding of divergences in perturbation theory, as well as their numerical treatment, is a necessary first step towards formulating such a program. The first objective of this dissertation is to clarify this issue, at least in second and fourth-order in perturbation theory. The work in this dissertation can provide guidance for the choice of counterterms in Discrete Light-Cone Quantization or the Tamm-Dancoff approach. A second objective of this work is the study of light-cone perturbation theory as a competitive tool for conducting perturbative Feynman diagram calculations. Feynman perturbation theory has become the most practical tool for computing cross sections in high energy physics and other physical properties of field theory. Although this standard covariant method has been applied to a great range of problems, computations beyond one-loop corrections are very difficult. Because of the algebraic complexity of the Feynman calculations in higher-order perturbation theory, it is desirable to automatize Feynman diagram calculations so that algebraic manipulation programs can carry out almost the entire calculation. This thesis presents a step in this direction. The technique we are elaborating on here is known as light-cone perturbation theory
End-point singularities of Feynman graphs on the light cone
We show that some Lorentz components of the Feynman integrals calculated in
terms of the light-cone variables may contain end-point singularities which
originate from the contribution of the big-circle integral in the complex k_
plane. These singularities appear in various types of diagrams (two-point
functions, three-point functions, etc) and provide the covariance of the
Feynman integrals on the light-cone. We propose a procedure for calculating
Feynman integrals which guarantees that the end-point singularities do not
appear in the light-cone representations of the invariant amplitudes.Comment: final version to appear in PLB; few references adde
A nonperturbative calculation of the electron's magnetic moment
In principle, the complete spectrum and bound-state wave functions of a
quantum field theory can be determined by finding the eigenvalues and
eigensolutions of its light-cone Hamiltonian. One of the challenges in
obtaining nonperturbative solutions for gauge theories such as QCD using
light-cone Hamiltonian methods is to renormalize the theory while preserving
Lorentz symmetries and gauge invariance. For example, the truncation of the
light-cone Fock space leads to uncompensated ultraviolet divergences. We
present two methods for consistently regularizing light-cone-quantized gauge
theories in Feynman and light-cone gauges: (1) the introduction of a spectrum
of Pauli-Villars fields which produces a finite theory while preserving Lorentz
invariance; (2) the augmentation of the gauge-theory Lagrangian with higher
derivatives. In the latter case, which is applicable to light-cone gauge (A^+ =
0), the A^- component of the gauge field is maintained as an independent degree
of freedom rather than a constraint. Finite-mass Pauli-Villars regulators can
also be used to compensate for neglected higher Fock states. As a test case, we
apply these regularization procedures to an approximate nonperturbative
computation of the anomalous magnetic moment of the electron in QED as a first
attempt to meet Feynman's famous challenge.Comment: 35 pages, elsart.cls, 3 figure
Precision Upsilon Spectroscopy from Nonrelativistic Lattice QCD
The spectrum of the Upsilon system is investigated using the Nonrelativistic
Lattice QCD approach to heavy quarks and ignoring light quark vacuum
polarization. We find good agreement with experiment for the Upsilon(1S),
Upsilon(2S), Upsilon(3S) and for the center of mass and fine structure of the
chi_b states. The lattice calculations predict b-bbar D-states with center of
mass at (10.20 +/- 0.07 +/- 0.03)GeV. Fitting procedures aimed at extracting
both ground and excited state energies are developed. We calculate a
nonperturbative dispersion mass for the Upsilon(1S) and compare with
tadpole-improved lattice perturbation theory.Comment: 8 pages, latex, SCRI-94-57, OHSTPY-HEP-T-94-00
Nonperturbative Light-Front QCD
In this work the determination of low-energy bound states in Quantum
Chromodynamics is recast so that it is linked to a weak-coupling problem. This
allows one to approach the solution with the same techniques which solve
Quantum Electrodynamics: namely, a combination of weak-coupling diagrams and
many-body quantum mechanics. The key to eliminating necessarily nonperturbative
effects is the use of a bare Hamiltonian in which quarks and gluons have
nonzero constituent masses rather than the zero masses of the current picture.
The use of constituent masses cuts off the growth of the running coupling
constant and makes it possible that the running coupling never leaves the
perturbative domain. For stabilization purposes an artificial potential is
added to the Hamiltonian, but with a coefficient that vanishes at the physical
value of the coupling constant. The weak-coupling approach potentially
reconciles the simplicity of the Constituent Quark Model with the complexities
of Quantum Chromodynamics. The penalty for achieving this perturbative picture
is the necessity of formulating the dynamics of QCD in light-front coordinates
and of dealing with the complexities of renormalization which such a
formulation entails. We describe the renormalization process first using a
qualitative phase space cell analysis, and we then set up a precise similarity
renormalization scheme with cutoffs on constituent momenta and exhibit
calculations to second order. We outline further computations that remain to be
carried out. There is an initial nonperturbative but nonrelativistic
calculation of the hadronic masses that determines the artificial potential,
with binding energies required to be fourth order in the coupling as in QED.
Next there is a calculation of the leading radiative corrections to these
masses, which requires our renormalization program. Then the real struggle of
finding the right extensions to perturbation theory to study the
strong-coupling behavior of bound states can begin.Comment: 56 pages (REVTEX), Report OSU-NT-94-28. (figures not included,
available via anaonymous ftp from pacific.mps.ohio-state.edu in subdirectory
pub/infolight/qcd
Light Front Quantization
An introductory overview on Light-Front quantization, with some emphasis on
recent achievements, is given. Light-Front quantization is the most promising
and physical tool to study deep inelastic scattering on the basis of quark
gluon degrees of freedom. The simplified vacuum structure (nontrivial vacuum
effects can only appear in zero-mode degrees of freedom) and the physical basis
allows for a description of hadrons that stays close to intuition. Recent
progress has ben made in understanding the connection between effective LF
Hamiltonians and nontrivial vacuum condesates. Discrete Light-Cone
Quantization, the transverse lattice and Light-Front Tamm-Dancoff (in
combination with renormalization group techniques) are the main tools for
exploring LF-Hamiltonians nonperturbatively.Comment: LATEX, 87 pages, postscript files for the figures or a postscript
file for the complete article (900 kB) available from the autho