31 research outputs found
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
Path Integral Approach to Two-Dimensional QCD in the Light-Front
Two-dimensional quantum cromodynamics in the light-front frame is studied
following hamiltonian methods. The theory is quantized using the path integral
formalism and an effective theory similar to the Nambu-Jona Lasinio model is
obtained. Confinement in two dimensions is derived analyzing directly the
constraints in the path integral.Comment: 13pp, Plain-TeX, Si-93-10, IF-UFRJ-93-13, USM-TH-6
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
Chiral Symmetry in Light-front QCD
The definition of chiral transformations in light-front field theory is very
different from the conventional form in equal-time formalism. We study the
consistency of chiral transformations and chiral symmetry in light-front QCD
and derive a complete new light-front axial-vector current for QCD. The
breaking of chiral symmetry in light-front QCD is only associated with helicity
flip interaction between quarks and gluons. Remarkably, the new axial-vector
current does not contain the pion pole part so that the associate chiral charge
smoothly describes pion transitions for various hadronic processes.Comment: 15 pages, no figure, JHEP style, added reference and corrected typos
and some changed conten
High Energy Theorems at Large-N
Sum rules for products of two, three and four QCD currents are derived using
chiral symmetry at infinite momentum in the large-N limit. These exact
relations among meson decay constants, axialvector couplings and masses
determine the asymptotic behavior of an infinite number of QCD correlators. The
familiar spectral function sum rules for products of two QCD currents are among
the relations derived. With this precise knowledge of asymptotic behavior, an
infinite number of large-N QCD correlators can be constructed using dispersion
relations. A detailed derivation is given of the exact large-N pion vector form
factor and forward pion-pion scattering amplitudes.Comment: 34 pages TeX and mtexsis.tex, 10 figures (uses epsf
Light Front Nuclear Physics: Toy Models, Static Sources and Tilted Light Front Coordinates
The principles behind the detailed results of a light-front mean field theory
of finite nuclei are elucidated by deriving the nucleon mode equation using a
simple general argument, based on the idea that a static source in equal time
coordinates corresponds to a moving source in light front coordinates. This
idea also allows us to solve several simple toy model examples: scalar field in
a box, 1+1 dimensional bag model, three-dimensional harmonic oscillator and the
Hulth\'en potential. The latter provide simplified versions of momentum
distributions and form factors of relevance to experiments. In particular, the
relativistic correction to the mean square radius of a nucleus is shown to be
very small. Solving these simple examples suggests another more general
approach-- the use of tilted light front coordinates. The simple examples are
made even simpler.Comment: 19 pages, references adde
A light-front coupled-cluster method for the nonperturbative solution of quantum field theories
We propose a new method for the nonperturbative solution of quantum field
theories and illustrate its use in the context of a light-front analog to the
Greenberg--Schweber model. The method is based on light-front quantization and
uses the exponential-operator technique of the many-body coupled-cluster
method. The formulation produces an effective Hamiltonian eigenvalue problem in
the valence Fock sector of the system of interest, combined with nonlinear
integral equations to be solved for the functions that define the effective
Hamiltonian. The method avoids the Fock-space truncations usually used in
nonperturbative light-front Hamiltonian methods and, therefore, does not suffer
from the spectator dependence, Fock-sector dependence, and uncanceled
divergences caused by such truncations.Comment: 11 pages, 4 figures, RevTeX 4.1; expanded description of method and
replaced QED with simpler model for illustratio
Spontaneous symmetry breaking of (1+1)-dimensional theory in light-front field theory (II)
We discuss spontaneous symmetry breaking of (1+1)-dimensional theory
in light-front field theory using a Tamm-Dancoff truncation. We show that, even
though light-front field theory has a simple vacuum state which is an
eigenstate of the full Hamiltonian, the field can develop a nonzero vacuum
expectation value. This occurs because the zero mode of the field must satisfy
an operator valued constraint equation. In the context of (1+1)-dimensional
theory we present solutions to the constraint equation using a
Tamm-Dancoff truncation to a finite number of particles and modes. We study the
behavior of the zero mode as a function of coupling and Fock space truncation.
The zero mode introduces new interactions into the Hamiltonian which breaks the
symmetry of the theory when the coupling is stronger than the critical
coupling.Comment: 25 page
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
Staggered fermions and chiral symmetry breaking in transverse lattice regulated QED
Staggered fermions are constructed for the transverse lattice regularization
scheme. The weak perturbation theory of transverse lattice non-compact QED is
developed in light-cone gauge, and we argue that for fixed lattice spacing this
theory is ultraviolet finite, order by order in perturbation theory. However,
by calculating the anomalous scaling dimension of the link fields, we find that
the interaction Hamiltonian becomes non-renormalizable for ,
where is the bare (lattice) QED coupling constant. We conjecture that
this is the critical point of the chiral symmetry breaking phase transition in
QED. Non-perturbative chiral symmetry breaking is then studied in the strong
coupling limit. The discrete remnant of chiral symmetry that remains on the
lattice is spontaneously broken, and the ground state to lowest order in the
strong coupling expansion corresponds to the classical ground state of the
two-dimensional spin one-half Heisenberg antiferromagnet.Comment: 30 pages, UFIFT-HEP-92-1