45 research outputs found
Quantum Hamiltonian Reduction of the Schwinger Model
We reexamine a unitary-transformation method of extracting a physical
Hamiltonian from a gauge field theory after quantizing all degrees of freedom
including redundant variables. We show that this {\it quantum Hamiltonian
reduction} method suffers from crucial modifications arising from
regularization of composite operators. We assess the effects of regularization
in the simplest gauge field theory, the Schwinger model. Without
regularization, the quantum reduction yields the identical Hamiltonian with the
classically reduced one. On the other hand, with regularization incorporated,
the resulting Hamiltonian of the quantum reduction disagrees with that of the
classical reduction. However, we find that the discrepancy is resolved by
redefinitions of fermion currents and that the results are again consistent
with those of the classical reduction.Comment: 23 pages, LaTeX file, UT-Komaba 94-
2D Yang-Mills Theory as a Matrix String Theory
Quantization of two-dimensional Yang-Mills theory on a torus in the gauge
where the field strength is diagonal leads to twisted sectors that are
completely analogous to the ones that originate long string states in Matrix
String Theory. If these sectors are taken into account the partition function
is different from the standard one found in the literature and the invariance
of the theory under modular transformations of the torus appears to hold in a
stronger sense. The twisted sectors are in one-to-one correspondence with the
coverings of the torus without branch points, so they define by themselves a
string theory. A possible duality between this string theory and the
Gross-Taylor string is discussed, and the problems that one encounters in
generalizing this approach to interacting strings are pointed out. This talk is
based on a previous paper by the same authors, but it contains some new results
and a better interpretation of the results already obtained.Comment: 11 pages, LaTeX, 2 figures included with epsf. Talk presented at the
2nd Conference on Quantum aspects of Gauge Theories, Supersymmetry and
Unification, Corfu, Greece, 21-26 September 199
Schwinger model on a half-line
We study the Schwinger model on a half-line in this paper. In particular, we
investigate the behavior of the chiral condensate near the edge of the line.
The effect of the chosen boundary condition is emphasized. The extension to the
finite temperature case is straightforward in our approach.Comment: 4 pages, no figure. Final version to be published on Phys. Rev.
The equation of state for two flavor QCD
We improve the calculation of the equation of state for two flavor QCD by
simulating on lattices at appropriate values of the couplings for the
deconfinement/chiral symmetry restoration crossover. For the
energy density rises rapidly to approximately 1 just after the
crossover( at this point). Comparing with our previous
result for ~\cite{eos}, we find large finite corrections as
expected from free field theory on finite lattices. We also provide formulae
for extracting the speed of sound from the measured quantities.Comment: Contribution to Lattice 95 proceedings (combines talks presented by
T. Blum and L. Karkkainen). LaTeX, 8 pages, uses espcrc2.sty, postscript
figures include
Critical Behavior at the Chiral Phase Transition
Quantum chromodynamics with two zero mass flavors is expected to exhibit a
phase transition with O(4) critical behavior. Fixing the universality class is
important for phenomenology and for facilitating the extrapolation of
simulation data to physical quark mass values. At Lattice '96 the Tsukuba and
Bielefeld groups reported results from new simulations with dynamical staggered
quarks at , which suggested a departure from the expected critical
behavior. We report observations of similar deviations and discuss efforts in
progress to understand this phenomenon.Comment: 3 pp, LaTeX with 6 encapsulated Postscript figures. Lattice '97
proceeding
Quantization of Field Theories Generalizing Gravity-Yang-Mills Systems on the Cylinder
Pure gravity and gauge theories in two dimensions are shown to be special
cases of a much more general class of field theories each of which is
characterized by a Poisson structure on a finite dimensional target space. A
general scheme for the quantization of these theories is formulated. Explicit
examples are studied in some detail. In particular gravity and gauge theories
with equivalent actions are compared. Big gauge transformations as well as the
condition of metric nondegeneracy in gravity turn out to cause significant
differences in the structure of the corresponding reduced phase spaces and the
quantum spectra of Dirac observables. For gravity coupled to SU(2) Yang
Mills the question of quantum dynamics (`problem of time') is addressed. [This
article is a contribution to the proceedings (to appear in LNP) of the 3rd
Baltic RIM Student Seminar (1993). Importance is attached to concrete examples.
A more abstract presentation of the ideas underlying this article (including
new developments) is found in hep-th/9405110.]Comment: 26, pages, TUW-94-
The Massive Multi-flavor Schwinger Model
QED with N species of massive fermions on a circle of circumference L is
analyzed by bosonization. The problem is reduced to the quantum mechanics of
the 2N fermionic and one gauge field zero modes on the circle, with nontrivial
interactions induced by the chiral anomaly and fermions masses. The solution is
given for N=2 and fermion masses (m) much smaller than the mass of the U(1)
boson with mass \mu=\sqrt{2e^2/\pi} when all fermions satisfy the same boundary
conditions. We show that the two limits m \go 0 and L \go \infty fail to
commute and that the behavior of the theory critically depends on the value of
mL|\cos\onehalf\theta| where \theta is the vacuum angle parameter. When the
volume is large \mu L \gg 1, the fermion condensate is
-(e^{4\gamma} m\mu^2 \cos^4\onehalf\theta/4\pi^3)^{1/3} or $-2e^\gamma m\mu L
\cos^2 \onehalf\theta /\pi^2 for mL(\mu L)^{1/2} |\cos\onehalf\theta| \gg 1 or
\ll 1, respectively. Its correlation function decays algebraically with a
critical exponent \eta=1 when m\cos\onehalf\theta=0.Comment: 16 pages, latex, uses epsf.sty; replaced with latex src
Pion and kaon physics with improved staggered quarks
We compute pseudoscalar meson masses and decay constants using staggered
quarks on lattices with three flavors of sea quarks and lattice spacings
fm and fm. We fit partially quenched results to
``staggered chiral perturbation theory'' formulae, thereby taking into account
the effects of taste-symmetry violations. Chiral logarithms are observed. From
the fits we calculate and , extract Gasser-Leutwyler parameters of
the chiral Lagrangian, and (modulo rather large perturbative errors) find the
light and strange quark masses.Comment: Lattice2003(spectrum); 3 pages, 1 eps figur
Thermodynamics for two flavor QCD
We conclude our analysis of the N_t=6 equation of state for two flavor QCD,
first described at last year's conference. We have obtained new runs at
am_q=0.025 and improved runs at am_q=0.0125. The results are extrapolated to
m_q=0, and we extract the speed of sound as well. We also present evidence for
a restoration of the SU(2) X SU(2) chiral symmetry just above the crossover,
but not of the axial U(1) chiral symmetry.Comment: Poster presented at LATTICE96(finite temperature). 4 pages, LaTeX
plus 5 encapsulated Postscript figure
Electromagnetic contributions to pseudoscalar masses
We report on the calculation by the MILC Collaboration of the electromagnetic effects on kaon
and pion masses. These masses are computed in QCD with dynamical (asqtad staggered) quarks
plus quenched photons at three lattice spacings varying from 0.12 to 0.06 fm. The masses are fit
to staggered chiral perturbation theory with NLO electromagnetic terms, as well as analytic terms
at higher order. We extrapolate the results to physical light-quark masses and to the continuum
limit. At the current stage of the analysis, most, but not all, of the systematic errors have been
estimated. The main goal is the comparison of kaon electromagnetic splittings to those of the
pion, i.e., an evaluation of the corrections to “Dashen’s theorem.” This in turn will allow us to
significantly reduce the systematic errors in our determination of m<sub>u</sub>/m<sub>d</sub>