99,763 research outputs found
Quantization of the Nonlinear Sigma Model Revisited
We revisit the subject of perturbatively quantizing the nonlinear sigma model
in two dimensions from a rigorous, mathematical point of view. Our main
contribution is to make precise the cohomological problem of eliminating
potential anomalies that may arise when trying to preserve symmetries under
quantization. The symmetries we consider are twofold: (i) diffeomorphism
covariance for a general target manifold; (ii) a transitive group of isometries
when the target manifold is a homogeneous space. We show that there are no
anomalies in case (i) and that (ii) is also anomaly-free under additional
assumptions on the target homogeneous space, in agreement with the work of
Friedan. We carry out some explicit computations for the -model. Finally,
we show how a suitable notion of the renormalization group establishes the
Ricci flow as the one loop renormalization group flow of the nonlinear sigma
model.Comment: 51 page
Dense-choice Counter Machines revisited
This paper clarifies the picture about Dense-choice Counter Machines, which
have been less studied than (discrete) Counter Machines. We revisit the
definition of "Dense Counter Machines" so that it now extends (discrete)
Counter Machines, and we provide new undecidability and decidability results.
Using the first-order additive mixed theory of reals and integers, we give a
logical characterization of the sets of configurations reachable by
reversal-bounded Dense-choice Counter Machines
Classically Time-Controlled Quantum Automata: Definition and Properties
In this paper we introduce classically time-controlled quantum automata or
CTQA, which is a reasonable modification of Moore-Crutchfield quantum finite
automata that uses time-dependent evolution and a "scheduler" defining how long
each Hamiltonian will run. Surprisingly enough, time-dependent evolution
provides a significant change in the computational power of quantum automata
with respect to a discrete quantum model. Indeed, we show that if a scheduler
is not computationally restricted, then a CTQA can decide the Halting problem.
In order to unearth the computational capabilities of CTQAs we study the case
of a computationally restricted scheduler. In particular we showed that
depending on the type of restriction imposed on the scheduler, a CTQA can (i)
recognize non-regular languages with cut-point, even in the presence of
Karp-Lipton advice, and (ii) recognize non-regular languages with
bounded-error. Furthermore, we study the closure of concatenation and union of
languages by introducing a new model of Moore-Crutchfield quantum finite
automata with a rotating tape head. CTQA presents itself as a new model of
computation that provides a different approach to a formal study of "classical
control, quantum data" schemes in quantum computing.Comment: Long revisited version of LNCS 11324:266-278, 2018 (TPNC 2018
Finite-size scaling above the upper critical dimension revisited: The case of the five-dimensional Ising model
Monte Carlo results for the moments of the magnetization distribution
of the nearest-neighbor Ising ferromagnet in a L^d geometry, where L (4 \leq L
\leq 22) is the linear dimension of a hypercubic lattice with periodic boundary
conditions in d=5 dimensions, are analyzed in the critical region and compared
to a recent theory of Chen and Dohm (CD) [X.S. Chen and V. Dohm, Int. J. Mod.
Phys. C (1998)]. We show that this finite-size scaling theory (formulated in
terms of two scaling variables) can account for the longstanding discrepancies
between Monte Carlo results and the so-called ``lowest-mode'' theory, which
uses a single scaling variable tL^{d/2} where t=T/T_c-1 is the temperature
distance from the critical temperature, only to a very limited extent. While
the CD theory gives a somewhat improved description of corrections to the
``lowest-mode'' results (to which the CD theory can easily be reduced in the
limit t \to 0, L \to \infty, tL^{d/2} fixed) for the fourth-order cumulant,
discrepancies are found for the susceptibility (L^d ). Reasons for these
problems are briefly discussed.Comment: 9 pages, 13 Encapsulated PostScript figures. To appear in Eur. Phys.
J. B. Also available as PDF file at
http://www.cond-mat.physik.uni-mainz.de/~luijten/erikpubs.htm
The Fubini-Furlan-Rossetti Sum Rule Revisited
The Fubini-Furlan-Rossetti sum rule for pion photoproduction on the nucleon
is evaluated by dispersion relations at constant t, and the corrections to the
sum rule due to the finite pion mass are calculated. Near threshold these
corrections turn out to be large due to pion-loop effects, whereas the sum rule
value is closely approached if the dispersion integrals are evaluated for
sub-threshold kinematics. This extension to the unphysical region provides a
unique framework to determine the low-energy constants of chiral perturbation
theory by global properties of the excitation spectrum.Comment: 12 pages, 7 postscript figures, EPJ style files include
- …