18 research outputs found
Topological field patterns of the Yang–Mills theory
AbstractIt is shown that the SO(3) gauge field configurations can be completely characterised by certain gauge invariant vector fields. The singularities of these vector fields describe the topological aspects of the gauge field configurations. The topological (or monopole) charge is expressed in terms of an Abelian vector potential
Reformulating Yang-Mills theory in terms of local gauge invariant variables
An explicit canonical transformation is constructed to relate the physical
subspace of Yang-Mills theory to the phase space of the ADM variables of
general relativity. This maps 3+1 dimensional Yang-Mills theory to local
evolution of metrics on 3 manifolds.Comment: Lattice 2000 (Gravity and Matrix Models) 3 pages, espcrc2.st
Half-monopoles and half-vortices in the Yang-Mills theory
It is demonstrated that there are smooth Yang-Mills potentials which
correspond to monopoles and vortices of one-half winding number. They are the
generic configurations, in contrast to the integral winding number
configurations like the 't Hooft-Polyakov monopole.Comment: 8 pages, 3 figures; references adde
Gauge-invariant dressed fermion propagator in massless QED_3
The infrared behaviour of the gauge-invariant dressed fermion propagator in
massless QED_3 is discussed for three choices of dressing. It is found that
only the propagator with the isotropic (in three Euclidean dimensions) choice
of dressing is acceptable as the physical fermion propagator. It is explained
that the negative anomalous dimension of this physical fermion does not
contradict any field-theoretical requirement.Comment: 10 pages; references added; minor changes in tex
Negative-Energy Spinors and the Fock Space of Lattice Fermions at Finite Chemical Potential
Recently it was suggested that the problem of species doubling with
Kogut-Susskind lattice fermions entails, at finite chemical potential, a
confusion of particles with antiparticles. What happens instead is that the
familiar correspondence of positive-energy spinors to particles, and of
negative-energy spinors to antiparticles, ceases to hold for the Kogut-Susskind
time derivative. To show this we highlight the role of the spinorial ``energy''
in the Osterwalder-Schrader reconstruction of the Fock space of non-interacting
lattice fermions at zero temperature and nonzero chemical potential. We
consider Kogut-Susskind fermions and, for comparison, fermions with an
asymmetric one-step time derivative.Comment: 14p
Infrared behaviour of massless QED in space-time dimensions 2 < d < 4
We show that the logarithmic infrared divergences in electron self-energy and
vertex function of massless QED in 2+1 dimensions can be removed at all orders
of 1/N by an appropriate choice of a non-local gauge. Thus the infrared
behaviour given by the leading order in 1/N is not modified by higher order
corrections. Our analysis gives a computational scheme for the Amati-Testa
model, resulting in a non-trivial conformal invariant field theory for all
space-time dimensions 2 < d < 4.Comment: 12 pages, uses axodraw.sty; added comments at the end, and one
reference; to appear in Phys. Lett.
Different definitions of the chemical potential with identical partition function in QCD on a lattice
It is shown that starting from one and the same transfer matrix formulation
of QCD on a lattice, it is possible to obtain both the action of Hasenfratz and
Karsch as well as an action where the chemical potential is not coupled to the
temporal links.Comment: 4 page
On the UV renormalizability of noncommutative field theories
UV/IR mixing is one of the most important features of noncommutative field
theories. As a consequence of this coupling of the UV and IR sectors, the
configuration of fields at the zero momentum limit in these theories is a very
singular configuration. We show that the renormalization conditions set at a
particular momentum configuration with a fixed number of zero momenta,
renormalizes the Green's functions for any general momenta only when this
configuration has same set of zero momenta. Therefore only when renormalization
conditions are set at a point where all the external momenta are nonzero, the
quantum theory is renormalizable for all values of nonzero momentum. This
arises as a result of different scaling behaviors of Green's functions with
respect to the UV cutoff () for configurations containing different
set of zero momenta. We study this in the noncommutative theory and
analyse similar results for the Gross-Neveu model at one loop level. We next
show this general feature using Wilsonian RG of Polchinski in the globally O(N)
symmetric scalar theory and prove the renormalizability of the theory to all
orders with an infrared cutoff. In the context of spontaneous symmetry breaking
(SSB) in noncommutative scalar theory, it is essential to note the different
scaling behaviors of Green's functions with respect to for different
set of zero momenta configurations. We show that in the broken phase of the
theory the Ward identities are satisfied to all orders only when one keeps an
infrared regulator by shifting to a nonconstant vacuum.Comment: 29 pages, 8 figures, uses JHEP.cls, references adde
Heavy-light mesons with staggered light quarks
We demonstrate the viability of improved staggered light quarks in studies of
heavy-light systems. Our method for constructing heavy-light operators exploits
the close relation between naive and staggered fermions. The new approach is
tested on quenched configurations using several staggered actionsn combined
with nonrelativistic heavy quarks. The B_s meson kinetic mass, the hyperfine
and 1P-1S splittings in B_s, and the decay constant f_{B_s} are calculated and
compared to previous quenched lattice studies. An important technical detail,
Bayesian curve-fitting, is discussed at length.Comment: 38 pages, figures included. v2: Entry in Table IX corrected and other
minor changes, version appearing in Phys. Rev.
The (LATTICE) QCD Potential and Running Coupling: How to Accurately Interpolate between Multi-Loop QCD and the String Picture
We present a simple parameterization of a running coupling constant, defined
via the static potential, that interpolates between 2-loop QCD in the UV and
the string prediction in the IR. Besides the usual \Lam-parameter and the
string tension, the coupling depends on one dimensionless parameter,
determining how fast the crossover from UV to IR behavior occurs (in principle
we know how to take into account any number of loops by adding more
parameters). Using a new Ansatz for the LATTICE potential in terms of the
continuum coupling, we can fit quenched and unquenched Monte Carlo results for
the potential down to ONE lattice spacing, and at the same time extract the
running coupling to high precision. We compare our Ansatz with 1-loop results
for the lattice potential, and use the coupling from our fits to quantitatively
check the accuracy of 2-loop evolution, compare with the Lepage-Mackenzie
estimate of the coupling extracted from the plaquette, and determine Sommer's
scale much more accurately than previously possible. For pure SU(3) we
find that the coupling scales on the percent level for .Comment: 47 pages, incl. 4 figures in LaTeX [Added remarks on correlated vs.
uncorrelated fits in sect. 4; corrected misprints; updated references.