71 research outputs found
Two-dimensional Quantum Gravity
This Ph.D. thesis pursues two goals: The study of the geometrical structure
of two-dimensional quantum gravity and in particular its fractal nature. To
address these questions we review the continuum formalism of quantum gravity
with special focus on the scaling properties of the theory. We discuss several
concepts of fractal dimensions which characterize the extrinsic and intrinsic
geometry of quantum gravity. This work is partly based on work done in
collaboration with Jan Ambj{\o}rn, Dimitrij Boulatov, Jakob L. Nielsen and
Yoshiyuki Watabiki (1997).
The other goal is the discussion of the discretization of quantum gravity and
to address the so called quantum failure of Regge calculus. We review dynamical
triangulations and show that it agrees with the continuum theory in two
dimensions. Then we discuss Regge calculus and prove that a continuum limit
cannot be taken in a sensible way and that it does not reproduce continuum
results. This work is partly based on work done in collaboration with Jan
Ambj{\o}rn, Jakob L. Nielsen and George Savvidy (1997).Comment: 90 pages, PhD thesis at the Faculty of Science, University of
Copenhage
Directed Percolation Universality in Asynchronous Evolution of Spatio-Temporal Intermittency
We present strong evidence that a coupled-map-lattice model for
spatio-temporal intermittency belongs to the universality class of directed
percolation when the updating rules are asynchronous, i.e. when only one
randomly chosen site is evolved at each time step. In contrast, when the system
is subjected to parallel updating, available numerical evidence suggests that
it does not belong to this universality class and that it is not even
universal. We argue that in the absence of periodic external forcing, the
asynchronous rule is the more physical.Comment: 12 pages, RevTeX, includes 6 figures, submitted to Physical Review
Letters; changed version includes a better physical motivation for
asynchronous updates, extra references and minor change
Schr\"odinger functional at N_f=-2
We study the Schr\"odinger functional coupling for lattice Yang-Mills theory
coupled to an improved bosonic spinor field, which corresponds to QCD with
minus two light flavors. This theory serves as a less costly testcase than QCD
for the scaling of the coupling.Comment: Lattice2001(improvement) 3 pages, 4 figure
Computation of the strong coupling in QCD with two dynamical flavours
We present a non-perturbative computation of the running of the coupling
alpha_s in QCD with two flavours of dynamical fermions in the Schroedinger
functional scheme. We improve our previous results by a reliable continuum
extrapolation. The Lambda-parameter characterizing the high-energy running is
related to the value of the coupling at low energy in the continuum limit. An
estimate of Lambda*r_0 is given using large-volume data with lattice spacings a
from 0.07 fm to 0.1 fm. It translates into Lambda_{MSbar}^{(2)}=245(16)(16) MeV
[assuming r_0=0.5 fm]. The last step still has to be improved to reduce the
uncertainty.Comment: 34 pages including figures and tables, latex2
Non-perturbative quark mass renormalization in two-flavor QCD
The running of renormalized quark masses is computed in lattice QCD with two
flavors of massless O(a) improved Wilson quarks. The regularization and flavor
independent factor that relates running quark masses to the renormalization
group invariant ones is evaluated in the Schroedinger Functional scheme. Using
existing data for the scale r_0 and the pseudoscalar meson masses, we define a
reference quark mass in QCD with two degenerate quark flavors. We then compute
the renormalization group invariant reference quark mass at three different
lattice spacings. Our estimate for the continuum value is converted to the
strange quark mass with the help of chiral perturbation theory.Comment: 25 pages, 6 figures; sections 1 and 4 rearranged, minor change to the
summary plo
Lattice HQET with exponentially improved statistical precision
We introduce an alternative discretization for static quarks on the lattice
retaining the O(a) improvement properties of the Eichten-Hill action. In this
formulation, statistical fluctuations are reduced by a factor which grows
exponentially with Euclidean time, x_0. For the first time, B-meson correlation
functions are computed with good statistical precision in the static
approximation for x_0>1 fm. At lattice spacings a \approx 0.1 fm, a \approx
0.08 fm and a \approx 0.07 fm the B_s-meson decay constant is determined in
static and quenched approximations. A correction due to the finite mass of the
b-quark is estimated by combining these static results with a recent
determination of F_Ds.Comment: Eqs. 14 and 15 corrected. Changes by up to 1 sigma in Table 1, Eq. 22
changed consequently. Result in Eq. 24 unchange
The charm quark's mass in quenched QCD
We present our preliminary result for the charmed quark mass, which follows
from taking the D_s and K meson masses from experiment and r0=0.5 fm (or,
equivalently F_K=160 MeV) to set the scale. For the renormalization group
invariant quark mass we obtain M_c = 1684(64) MeV, which translates to
m_c(m_c)= 1314 (40)(20)(7) MeV for the running mass in the MSbar scheme.
Renormalization is treated non-perturbatively, and the continuum limit has been
taken, so that the only uncontrolled systematic error consists in the use of
the quenched approximation.Comment: Lattice2001(spectrum), 3 page
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