6 research outputs found
Noncommutativity from spectral flow
We investigate the transition from second to first order systems. This
transforms configuration space into phase space and hence introduces
noncommutativity in the former. Quantum mechanically, the transition may be
described in terms of spectral flow. Gaps in the energy or mass spectrum may
become large which effectively truncates the available state space. Using both
operator and path integral languages we explicitly discuss examples in quantum
mechanics, (light-front) quantum field theory and string theory.Comment: 31 pages, one Postscript figur
Light-Front Quantum Chromodynamics: A framework for the analysis of hadron physics
White Paper of International Light Cone Advisory CommitteeAn outstanding goal of physics is to find solutions that describe hadrons in the theory of strong interactions, Quantum Chromodynamics (QCD). For this goal, the light-front Hamiltonian formulation of QCD (LFQCD) is a complementary approach to the well-established lattice gauge method. LFQCD offers access to the hadrons' nonperturbative quark and gluon amplitudes, which are directly testable in experiments at existing and future facilities. We present an overview of the promises and challenges of LFQCD in the context of unsolved issues in QCD that require broadened and accelerated investigation. We identify specific goals of this approach and address its quantifiable uncertainties
Pion light-cone wave function and pion distribution amplitude in the Nambu-Jona-Lasinio model
We compute the pion light-cone wave function and the pion quark distribution
amplitude in the Nambu-Jona-Lasinio model. We use the Pauli-Villars
regularization method and as a result the distribution amplitude satisfies
proper normalization and crossing properties. In the chiral limit we obtain the
simple results, namely phi_pi(x)=1 for the pion distribution amplitude, and
= -M / f_pi^2 for the second moment of the pion light-cone
wave function, where M is the constituent quark mass and f_pi is the pion decay
constant. After the QCD Gegenbauer evolution of the pion distribution amplitude
good end-point behavior is recovered, and a satisfactory agreement with the
analysis of the experimental data from CLEO is achieved. This allows us to
determine the momentum scale corresponding to our model calculation, which is
close to the value Q_0 = 313 MeV obtained earlier from the analogous analysis
of the pion parton distribution function. The value of is, after the
QCD evolution, around (400 MeV)^2. In addition, the model predicts a linear
integral relation between the pion distribution amplitude and the parton
distribution function of the pion, which holds at the leading-order QCD
evolution.Comment: mistake in Eq.(38) correcte
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