3,135 research outputs found
Renormalization of an effective Light-Cone QCD-inspired theory for the Pion and other Mesons
The renormalization of the effective QCD-Hamiltonian theory for the
quark-antiquark channel is performed in terms of a renormalized or fixed-point
Hamiltonian that leads to subtracted dynamical equations. The fixed
point-Hamiltonian brings the renormalization conditions as well as the
counterterms that render the theory finite. The approach is renormalization
group invariant. The parameters of the renormalized effective QCD-Hamiltonian
comes from the pion mass and radius, for a given constituent quark mass. The 1s
and excited 2s states of are calculated as a function of the mass of
the quark being s, c or b, and compared to the experimental values.Comment: 39 pages, 10 figure
On the Size of Hadrons
The form factor and the mean-square radius of the pion are calculated
analytically from a parametrized form of a wave function. The
numerical wave function was obtained previously by solving numerically an
eigenvalue equation for the pion in a particular model. The analytical formulas
are of more general interest than just be valid for the pion and can be
generalized to the case with unequal quark masses. Two different
parametrizations are investigated. Because of the highly relativistic problem,
noticable deviations from a non-relativistic formula are obtained.Comment: 14 pages, minor typos corrected, several points clarified, results
unchange
Exact solutions to Pauli-Villars-regulated field theories
We present a new class of quantum field theories which are exactly solvable.
The theories are generated by introducing Pauli-Villars fermionic and bosonic
fields with masses degenerate with the physical positive metric fields. An
algorithm is given to compute the spectrum and corresponding eigensolutions. We
also give the operator solution for a particular case and use it to illustrate
some of the tenets of light-cone quantization. Since the solutions of the
solvable theory contain ghost quanta, these theories are unphysical. However,
we also discuss how perturbation theory in the difference between the masses of
the physical and Pauli-Villars particles could be developed, thus generating
physical theories. The existence of explicit solutions of the solvable theory
also allows one to study the relationship between the equal-time and light-cone
vacua and eigensolutions.Comment: 20 pages, REVTeX; minor corrections to normalization
Interference in Bohmian Mechanics with Complex Action
In recent years, intensive effort has gone into developing numerical tools
for exact quantum mechanical calculations that are based on Bohmian mechanics.
As part of this effort we have recently developed as alternative formulation of
Bohmian mechanics in which the quantum action, S, is taken to be complex [JCP
{125}, 231103 (2006)]. In the alternative formulation there is a significant
reduction in the magnitude of the quantum force as compared with the
conventional Bohmian formulation, at the price of propagating complex
trajectories. In this paper we show that Bohmian mechanics with complex action
is able to overcome the main computational limitation of conventional Bohmian
methods -- the propagation of wavefunctions once nodes set in. In the vicinity
of nodes, the quantum force in conventional Bohmian formulations exhibits rapid
oscillations that pose severe difficulties for existing numerical schemes. We
show that within complex Bohmian mechanics, multiple complex initial conditions
can lead to the same real final position, allowing for the description of nodes
as a sum of the contribution from two or more crossing trajectories. The idea
is illustrated on the reflection amplitude from a one-dimensional Eckart
barrier. We believe that trajectory crossing, although in contradiction to the
conventional Bohmian trajectory interpretation, provides an important new tool
for dealing with the nodal problem in Bohmian methods
Noncommutative Gauge Theory on the q-Deformed Euclidean Plane
In this talk we recall some concepts of Noncommutative Gauge Theories. In
particular, we discuss the q-deformed two-dimensional Euclidean Plane which is
covariant with respect to the q-deformed Euclidean group. A Seiberg-Witten map
is constructed to express noncommutative fields in terms of their commutative
counterparts.Comment: 5 pages; Talk given by Frank Meyer at the 9th Adriatic Meeting,
September 4th-14th, 2003, Dubrovni
Vacuum polarization induced by a uniformly accelerated charge
We consider a point charge fixed in the Rindler coordinates which describe a
uniformly accelerated frame. We determine an integral expression of the induced
charge density due to the vacuum polarization at the first order in the fine
structure constant. In the case where the acceleration is weak, we give
explicitly the induced electrostatic potential.Comment: 13 pages, latex, no figures, to appear in Int. J. Theor. Phys
Finiteness Conditions for Light-Front Hamiltonians
In the context of simple models, it is shown that demanding finiteness for
physical masses with respect to a longitudinal cutoff, can be used to fix the
ambiguity in the renormalization of fermions masses in the Hamiltonian
light-front formulation. Difficulties that arise in applications of finiteness
conditions to discrete light-cone quantization are discussed.Comment: REVTEX, 9 page
Universal description of S-wave meson spectra in a renormalized light-cone QCD-inspired model
A light-cone QCD-inspired model, with the mass squared operator consisting of
a harmonic oscillator potential as confinement and a Dirac-delta interaction,
is used to study the S-wave meson spectra. The two parameters of the harmonic
potential and quark masses are fixed by masses of rho(770), rho(1450), J/psi,
psi(2S), K*(892) and B*. We apply a renormalization method to define the model,
in which the pseudo-scalar ground state mass fixes the renormalized strength of
the Dirac-delta interaction. The model presents an universal and satisfactory
description of both singlet and triplet states of S-wave mesons and the
corresponding radial excitations.Comment: RevTeX, 17 pages, 7 eps figures, to be published in Phys. Rev.
Tube Model for Light-Front QCD
We propose the tube model as a first step in solving the bound state problem
in light-front QCD. In this approach we neglect transverse variations of the
fields, producing a model with 1+1 dimensional dynamics. We then solve the two,
three, and four particle sectors of the model for the case of pure glue SU(3).
We study convergence to the continuum limit and various properties of the
spectrum.Comment: 29 page
Non-Perturbative Spectrum of Two Dimensional (1,1) Super Yang-Mills at Finite and Large N
We consider the dimensional reduction of N = 1 SYM_{2+1} to 1+1 dimensions,
which has (1,1) supersymmetry. The gauge groups we consider are U(N) and SU(N),
where N is a finite variable. We implement Discrete Light-Cone Quantization to
determine non-perturbatively the bound states in this theory. A careful
analysis of the spectrum is performed at various values of N, including the
case where N is large (but finite), allowing a precise measurement of the 1/N
effects in the quantum theory. The low energy sector of the theory is shown to
be dominated by string-like states. The techniques developed here may be
applied to any two dimensional field theory with or without supersymmetry.Comment: LaTex 18 pages; 5 Encapsulated PostScript figure
- …