196 research outputs found
General Form of the Color Potential Produced by Color Charges of the Quark
Constant electric charge satisfies the continuity equation where is the current density of the electron.
However, the Yang-Mills color current density of the quark
satisfies the equation which is not a continuity
equation () which implies that a color charge
of the quark is not constant but it is time dependent where
are color indices. In this paper we derive general form of color
potential produced by color charges of the quark. We find that the general form
of the color potential produced by the color charges of the quark at rest is
given by \Phi^a(x) =A_0^a(t,{\bf x}) =\frac{q^b(t-\frac{r}{c})}{r}\[\frac{{\rm
exp}[g\int dr \frac{Q(t-\frac{r}{c})}{r}] -1}{g \int dr
\frac{Q(t-\frac{r}{c})}{r}}\]_{ab} where integration is an indefinite
integration, ~~ , ~~, ~~ is the retarded time, ~~ is the speed
of light, ~~ is the position of the quark at the retarded
time and the repeated color indices (=1,2,...8) are summed. For constant
color charge we reproduce the Coulomb-like potential
which is consistent with the Maxwell theory where
constant electric charge produces the Coulomb potential
.Comment: Final version, two more sections added, 45 pages latex, accepted for
publication in JHE
A gauge invariant and string independent fermion correlator in the Schwinger model
We introduce a gauge invariant and string independent two-point fermion
correlator which is analyzed in the context of the Schwinger model (QED_2). We
also derive an effective infrared worldline action for this correlator, thus
enabling the computation of its infrared behavior. Finally, we briefly discuss
possible perspectives for the string independent correlator in the QED_3
effective models for the normal state of HTc superconductors.Comment: 14 pages, LaTe
Some Variations on Maxwell's Equations
In the first sections of this article, we discuss two variations on Maxwell's
equations that have been introduced in earlier work--a class of nonlinear
Maxwell theories with well-defined Galilean limits (and correspondingly
generalized Yang-Mills equations), and a linear modification motivated by the
coupling of the electromagnetic potential with a certain nonlinear Schroedinger
equation. In the final section, revisiting an old idea of Lorentz, we write
Maxwell's equations for a theory in which the electrostatic force of repulsion
between like charges differs fundamentally in magnitude from the electrostatic
force of attraction between unlike charges. We elaborate on Lorentz'
description by means of electric and magnetic field strengths, whose governing
equations separate into two fully relativistic Maxwell systems--one describing
ordinary electromagnetism, and the other describing a universally attractive or
repulsive long-range force. If such a force cannot be ruled out {\it a priori}
by known physical principles, its magnitude should be determined or bounded
experimentally. Were it to exist, interesting possibilities go beyond Lorentz'
early conjecture of a relation to (Newtonian) gravity.Comment: 26 pages, submitted to a volume in preparation to honor Gerard Emch
v. 2: discussion revised, factors of 4\pi corrected in some equation
Thirring Model with Non-conserved Chiral Charge
We study the Abelian Thirring Model when the fermionic fields have
non-conserved chiral charge: . One of the main features
we find for this model is the dependence of the Virasoro central charge on both
the Thirring coupling constant and . We show how to evaluate correlation
functions and in particular we compute the conformal dimensions for fermions
and fermionic bilinears, which depend on the fermionic chiral charge. Finally
we build primary fields with arbitrary conformal weight.Comment: pages 1
New extended high temperature series for the N-vector spin models on three-dimensional bipartite lattices
High temperature expansions for the susceptibility and the second correlation
moment of the classical N-vector model (O(N) symmetric Heisenberg model) on the
sc and the bcc lattices are extended to order for arbitrary N. For
N= 2,3,4.. we present revised estimates of the critical parameters from the
newly computed coefficients.Comment: 11 pages, latex, no figures, to appear in Phys. Rev.
Schwinger Model Green functions with topological effects
The fermion propagator and the 4-fermion Green function in the massless QED2
are explicitly found with topological effects taken into account. The
corrections due to instanton sectors k=+1,-1, contributing to the propagator,
are shown to be just the homogenous terms admitted by the Dyson-Schwinger
equation for S. In the case of the 4-fermion function also sectors k=+2,-2 are
included into consideration. The quark condensates are then calculated and are
shown to satisfy cluster property. The theta-dependence exhibited by the Green
functions corresponds to and may be removed by performing certain chiral gauge
transformation.Comment: 16 pages, in REVTE
Multiflavor Correlation Functions in non-Abelian Gauge Theories at Finite Density in two dimensions
We compute vacuum expectation values of products of fermion bilinears for
two-dimensional Quantum Chromodynamics at finite flavored fermion densities. We
introduce the chemical potential as an external charge distribution within the
path-integral approach and carefully analyse the contribution of different
topological sectors to fermion correlators. We show the existence of chiral
condensates exhibiting an oscillatory inhomogeneous behavior as a function of a
chemical potential matrix. This result is exact and goes in the same direction
as the behavior found in QCD_4 within the large N approximation.Comment: 28 pages Latex (3 pages added and other minor changes) to appear in
Phys.Rev.
N-vector spin models on the sc and the bcc lattices: a study of the critical behavior of the susceptibility and of the correlation length by high temperature series extended to order beta^{21}
High temperature expansions for the free energy, the susceptibility and the
second correlation moment of the classical N-vector model [also known as the
O(N) symmetric classical spin Heisenberg model or as the lattice O(N) nonlinear
sigma model] on the sc and the bcc lattices are extended to order beta^{21} for
arbitrary N. The series for the second field derivative of the susceptibility
is extended to order beta^{17}. An analysis of the newly computed series for
the susceptibility and the (second moment) correlation length yields updated
estimates of the critical parameters for various values of the spin
dimensionality N, including N=0 [the self-avoiding walk model], N=1 [the Ising
spin 1/2 model], N=2 [the XY model], N=3 [the Heisenberg model]. For all values
of N, we confirm a good agreement with the present renormalization group
estimates. A study of the series for the other observables will appear in a
forthcoming paper.Comment: Revised version to appear in Phys. Rev. B Sept. 1997. Revisions
include an improved series analysis biased with perturbative values of the
scaling correction exponents computed by A. I. Sokolov. Added a reference to
estimates of exponents for the Ising Model. Abridged text of 19 pages, latex,
no figures, no tables of series coefficient
Renormalized couplings and scaling correction amplitudes in the N-vector spin models on the sc and the bcc lattices
For the classical N-vector model, with arbitrary N, we have computed through
order \beta^{17} the high temperature expansions of the second field derivative
of the susceptibility \chi_4(N,\beta) on the simple cubic and on the body
centered cubic lattices. (The N-vector model is also known as the O(N)
symmetric classical spin Heisenberg model or, in quantum field theory, as the
lattice
O(N) nonlinear sigma model.) By analyzing the expansion of \chi_4(N,\beta) on
the two lattices, and by carefully allowing for the corrections to scaling, we
obtain updated estimates of the critical parameters and more accurate tests of
the hyperscaling relation d\nu(N) +\gamma(N) -2\Delta_4(N)=0 for a range of
values of the spin dimensionality N, including
N=0 [the self-avoiding walk model], N=1 [the Ising spin 1/2 model],
N=2 [the XY model], N=3 [the classical Heisenberg model]. Using the recently
extended series for the susceptibility and for the second correlation moment,
we also compute the dimensionless renormalized four point coupling constants
and some universal ratios of scaling correction amplitudes in fair agreement
with recent renormalization group estimates.Comment: 23 pages, latex, no figure
Critical specific heats of the N-vector spin models on the sc and the bcc lattices
We have computed through order the high-temperature expansions
for the nearest-neighbor spin correlation function of the
classical N-vector model, with general N, on the simple-cubic and on the
body-centered-cubic lattices.
For this model, also known in quantum field theory as the lattice O(N)
nonlinear sigma model, we have presented in previous papers extended expansions
of the susceptibility, of its second field derivative and of the second moment
of the correlation function.
Here we study the internal specific energy and the specific heat
, obtaining new estimates of the critical parameters and therefore
a more accurate direct test of the hyperscaling relation on a range of values of the spin dimensionality N, including N=0
[the self-avoiding walk model], N=1 [the Ising spin 1/2 model], N=2 [the XY
model], N=3 [the classical Heisenberg model]. By the newly extended series, we
also compute the universal combination of critical amplitudes usually denoted
by , in fair agreement with renormalization group estimates.Comment: 15 pages, latex, no figure
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