2,961 research outputs found
Involution and Constrained Dynamics I: The Dirac Approach
We study the theory of systems with constraints from the point of view of the
formal theory of partial differential equations. For finite-dimensional systems
we show that the Dirac algorithm completes the equations of motion to an
involutive system. We discuss the implications of this identification for field
theories and argue that the involution analysis is more general and flexible
than the Dirac approach. We also derive intrinsic expressions for the number of
degrees of freedom.Comment: 28 pages, latex, no figure
Lattice artefacts and the running of the coupling constant
We study the running of the L\"uscher-Weisz-Wolff (LWW) coupling constant in
the two dimensional O(3) nonlinear model. To investigate the continuum
limit we refine the lattice spacing from the value used by LWW up
to . We find that the lattice artefacts are much larger than
estimated by LWW and that most likely the coupling constant runs slower than
predicted by perturbation theory. A precise determination of the running in the
continuum limit would require a controlled ansatz of extrapolation, which, we
argue, is not presently available.Comment: 4 pages, 4 figures. To address the criticism that we are studying a
different quantitiy than Luscher, Weisz and Wolff originally did, we
introduced a new equation (2), a new paragraph discussing this issue and a
new figure comparing the results obtained with our prescription to that
obtained with the original one of Luscher, Weisz and Wolf
Functional Integral Construction of the Thirring model: axioms verification and massless limit
We construct a QFT for the Thirring model for any value of the mass in a
functional integral approach, by proving that a set of Grassmann integrals
converges, as the cutoffs are removed and for a proper choice of the bare
parameters, to a set of Schwinger functions verifying the Osterwalder-Schrader
axioms. The corresponding Ward Identities have anomalies which are not linear
in the coupling and which violate the anomaly non-renormalization property.
Additional anomalies are present in the closed equation for the interacting
propagator, obtained by combining a Schwinger-Dyson equation with Ward
Identities.Comment: 55 pages, 9 figure
Continuum Limit of Spin Models with Continuous Symmetry and Conformal Quantum Field Theory
According to the standard classification of Conformal Quantum Field Theory
(CQFT) in two dimensions, the massless continuum limit of the model at
the Kosterlitz-Thouless (KT) transition point should be given by the massless
free scalar field; in particular the Noether current of the model should be
proportional to (the dual of) the gradient of the massless free scalar field,
reflecting a symmetry enhanced from to . More
generally, the massless continuum limit of a spin model with a symmetry given
by a Lie group should have an enhanced symmetry . We point out
that the arguments leading to this conclusion contain two serious gaps: i) the
possibility of `nontrivial local cohomology' and ii) the possibility that the
current is an ultralocal field. For the model we give analytic
arguments which rule out the first possibility and use numerical methods to
dispose of the second one. We conclude that the standard CQFT predictions
appear to be borne out in the model, but give an example where they
would fail. We also point out that all our arguments apply equally well to any
symmetric spin model, provided it has a critical point at a finite
temperature.Comment: 19 page
Production of 26Al in stellar hydrogen-burning environments: spectroscopic properties of states in 27Si
Model predictions of the amount of the radioisotope 26Al produced in
hydrogen-burning environments require reliable estimates of the thermonuclear
rates for the 26gAl(p,{\gamma})27Si and 26mAl(p,{\gamma})27Si reactions. These
rates depend upon the spectroscopic properties of states in 27Si within about 1
MeV of the 26gAl+p threshold (Sp = 7463 keV). We have studied the
28Si(3He,{\alpha})27Si reaction at 25 MeV using a high-resolution
quadrupole-dipole-dipole-dipole magnetic spectrograph. For the first time with
a transfer reaction, we have constrained J{\pi} values for states in 27Si over
Ex = 7.0 - 8.1 MeV through angular distribution measurements. Aside from a few
important cases, we generally confirm the energies and spin-parity assignments
reported in a recent {\gamma}-ray spectroscopy study. The magnitudes of neutron
spectroscopic factors determined from shell-model calculations are in
reasonable agreement with our experimental values extracted using this
reaction.Comment: accepted for publication in Phys. Rev.
Spectroscopy of Ne for the thermonuclear O()Ne and F()O reaction rates
Uncertainties in the thermonuclear rates of the
O()Ne and F()O reactions
affect model predictions of light curves from type I X-ray bursts and the
amount of the observable radioisotope F produced in classical novae,
respectively. To address these uncertainties, we have studied the nuclear
structure of Ne over MeV and MeV using
the F(He,t)Ne reaction. We find the values of the
4.14 and 4.20 MeV levels to be consistent with and
respectively, in contrast to previous assumptions. We confirm the recently
observed triplet of states around 6.4 MeV, and find evidence that the state at
6.29 MeV, just below the proton threshold, is either broad or a doublet. Our
data also suggest that predicted but yet unobserved levels may exist near the
6.86 MeV state. Higher resolution experiments are urgently needed to further
clarify the structure of Ne around the proton threshold before a
reliable F()O rate for nova models can be determined.Comment: 5 pages, 3 figures, Phys. Rev. C (in press
Electrically and Magnetically Charged States and Particles in the 2+1-Dimensional Z_N-Higgs Gauge Model
Electrically as well as magnetically charged states are constructed in the
2+1-dimensional Euclidean Z_N-Higgs lattice gauge model, the former following
ideas of Fredenhagen and Marcu and the latter using duality transformations on
the algebra of observables. The existence of electrically and of magnetically
charged particles is also established. With this work we prepare the ground for
the constructive study of anyonic statistics of multiparticle scattering states
of electrically and magnetically charged particles in this model (work in
progress).Comment: 57 pages, Sfb 288 Preprint No. 109. To appear in Commun. Math. Phys.
About the file: This is a uuencoded, "gzip-ed" postscript file. It is about
300kB large. The original ps file is about 700kB large. All figures are
included. The LaTeX sources ou even hard copies can be required to the
authors at [email protected] or Freie Universitaet Berlin.
Institut fuer Theoretische Physik. Arnimallee 14. Berlin 14195 German
Invariant measure in hot gauge theories
We investigate properties of the invariant measure for the gauge field
in finite temperature gauge theories both on the lattice and in the continuum
theory. We have found the cancellation of the naive measure in both cases. The
result is quite general and holds at any finite temperature. We demonstrate,
however, that there is no cancellation at any temperature for the invariant
measure contribution understood as Z(N) symmetrical distribution of gauge field
configurations. The spontaneous breakdown of Z(N) global symmetry is entirely
due to the potential energy term of the gluonic interaction in the effective
potential. The effects of this measure on the effective action, mechanism of
confinement and condensation are discussed.Comment: Latex file, 65.5kB, no figure
Remark on Pauli-Villars Lagrangian on the Lattice
It is interesting to superimpose the Pauli-Villars regularization on the
lattice regularization. We illustrate how this scheme works by evaluating the
axial anomaly in a simple lattice fermion model, the Pauli-Villars Lagrangian
with a gauge non-invariant Wilson term. The gauge non-invariance of the axial
anomaly, caused by the Wilson term, is remedied by a compensation among
Pauli-Villars regulators in the continuum limit. A subtlety in Frolov-Slavnov's
scheme for an odd number of chiral fermions in an anomaly free complex gauge
representation, which requires an infinite number of regulators, is briefly
mentioned.Comment: 14 pages, Phyzzx. The final version to appear in Phys. Rev.
Fermion kinetics in the Falicov-Kimball limit of the three-band Emery model
The three-band Emery model is reduced to a single-particle quantum model of
Falicov-Kimball type, by allowing only up-spins to hop, and forbidding double
occupation by projection. It is used to study the effects of geometric
obstruction on mobile fermions in thermodynamic equilibrium. For low hopping
overlap, there appears a plateau in the entropy, due to charge correlations,
and related to real-space disorder. For large overlap, the equilibrium
thermopower susceptibility remains anomalous, with a sign opposite to the one
predicted from the single-particle density of states. The heat capacity and
non-Fermi liquid response are discussed in the context of similar results in
the literature. All results are obtained by evaluation of an effective
single-particle free-energy operator in closed form. The method to obtain this
operator is described in detail.Comment: New calculations, method explained in detail, 16 pages, 9 figure
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