16 research outputs found
Constraints and Hamiltonian in Light-Front Quantized Field Theory
Self-consistent Hamiltonian formulation of scalar theory on the null plane is
constructed following Dirac method. The theory contains also {\it constraint
equations}. They would give, if solved, to a nonlinear and nonlocal
Hamiltonian. The constraints lead us in the continuum to a different
description of spontaneous symmetry breaking since, the symmetry generators now
annihilate the vacuum. In two examples where the procedure lacks
self-consistency, the corresponding theories are known ill-defined from
equal-time quantization. This lends support to the method adopted where both
the background field and the fluctuation above it are treated as dynamical
variables on the null plane. We let the self-consistency of the Dirac procedure
determine their properties in the quantized theory. The results following from
the continuum and the discretized formulations in the infinite volume limit do
agree.Comment: 11 pages, Padova University preprint DFPF/92/TH/52 (December '92
The Role of Zero-Modes in the Canonical Quantization of Heavy-Fermion QED in Light-Cone Coordinates
Four-dimensional heavy-fermion QED is studied in light-cone coordinates with
(anti-)periodic field boundary conditions. We carry out a consistent light-cone
canonical quantization of this model using the Dirac algorithm for a system
with first- and second-class constraints. To examine the role of the zero
modes, we consider the quantization procedure in {the }zero-mode {and the
non-zero-mode} sectors separately. In both sectors we obtain the physical
variables and their canonical commutation relations. The physical Hamiltonian
is constructed via a step-by-step exclusion of the unphysical degrees of
freedom. An example using this Hamiltonian in which the zero modes play a role
is the verification of the correct Coulomb potential between two heavy
fermions.Comment: 22 pages, CWRUTH-93-5 (Latex
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
Light-Front View of The Axial Anomaly
Motivated by an apparent puzzle of the light-front vacua incompatible with
the axial anomaly, we have considered the two-dimensional massless Schwinger
model for an arbitrary interpolating angle of the quantization surface. By
examining spectral deformation of the Dirac sea under an external electric
field semiclassically, we have found that the axial anomaly is quantization
angle independent. This indicates an intricate nontrivial vacuum structure
present even in the light-front limit.Comment: 12 pages, REVTEX, one figure postscript file encode
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