671 research outputs found
Renormalization and Essential Singularity
In usual dimensional counting, momentum has dimension one. But a function
f(x), when differentiated n times, does not always behave like one with its
power smaller by n. This inevitable uncertainty may be essential in general
theory of renormalization, including quantum gravity. As an example, we
classify possible singularities of a potential for the Schr\"{o}dinger
equation, assuming that the potential V has at least one class eigen
function. The result crucially depends on the analytic property of the eigen
function near its 0 point.Comment: 12 pages, no figures, PTPTeX with amsfonts. 2 pages added for detail
Algebra versus analysis in the theory of flexible polyhedra
Two basic theorems of the theory of flexible polyhedra were proven by
completely different methods: R. Alexander used analysis, namely, the Stokes
theorem, to prove that the total mean curvature remains constant during the
flex, while I.Kh. Sabitov used algebra, namely, the theory of resultants, to
prove that the oriented volume remains constant during the flex. We show that
none of these methods can be used to prove the both theorems. As a by-product,
we prove that the total mean curvature of any polyhedron in the Euclidean
3-space is not an algebraic function of its edge lengths.Comment: 5 pages, 5 figures; condition (iii) in Theorem 5 is correcte
Regular vs. classical M\"obius transformations of the quaternionic unit ball
The regular fractional transformations of the extended quaternionic space
have been recently introduced as variants of the classical linear fractional
transformations. These variants have the advantage of being included in the
class of slice regular functions, introduced by Gentili and Struppa in 2006, so
that they can be studied with the useful tools available in this theory. We
first consider their general properties, then focus on the regular M\"obius
transformations of the quaternionic unit ball B, comparing the latter with
their classical analogs. In particular we study the relation between the
regular M\"obius transformations and the Poincar\'e metric of B, which is
preserved by the classical M\"obius transformations. Furthermore, we announce a
result that is a quaternionic analog of the Schwarz-Pick lemma.Comment: 14 page
On the Semi-Relative Condition for Closed (TOPOLOGICAL) Strings
We provide a simple lagrangian interpretation of the meaning of the
semi-relative condition in closed string theory. Namely, we show how the
semi-relative condition is equivalent to the requirement that physical
operators be cohomology classes of the BRS operators acting on the space of
local fields {\it covariant} under world-sheet reparametrizations. States
trivial in the absolute BRS cohomology but not in the semi-relative one are
explicitly seen to correspond to BRS variations of operators which are not
globally defined world-sheet tensors. We derive the covariant expressions for
the observables of topological gravity. We use them to prove a formula that
equates the expectation value of the gravitational descendant of ghost number 4
to the integral over the moduli space of the Weil-Peterson K\"ahler form.Comment: 10 pages, harvmac, CERN-TH-7084/93, GEF-TH-21/199
Constraints on the form factors for K --> pi l nu and implications for V_us
Rigorous bounds are established for the expansion coefficients governing the
shape of semileptonic K-->pi form factors. The constraints enforced by
experimental data from tau-->K pi nu eliminate uncertainties associated with
model parameterizations in the determination of |V_us|. The results support the
validity of a powerful expansion that can be applied to other semileptonic
transitions.Comment: 5 pages, 3 figures; references added, version to appear in Phys. Rev.
D alongside hep-ex/060805
On an inverse problem for anisotropic conductivity in the plane
Let be a bounded domain with smooth
boundary and a smooth anisotropic conductivity on .
Starting from the Dirichlet-to-Neumann operator on
, we give an explicit procedure to find a unique domain
, an isotropic conductivity on and the boundary
values of a quasiconformal diffeomorphism which
transforms into .Comment: 9 pages, no figur
Fluctuation force exerted by a planar self-avoiding polymer
Using results from Schramm Loewner evolution (SLE), we give the expression of
the fluctuation-induced force exerted by a polymer on a small impenetrable
disk, in various 2-dimensional domain geometries. We generalize to two polymers
and examine whether the fluctuation force can trap the object into a stable
equilibrium. We compute the force exerted on objects at the domain boundary,
and the force mediated by the polymer between such objects. The results can
straightforwardly be extended to any SLE interface, including Ising,
percolation, and loop-erased random walks. Some are relevant for extremal value
statistics.Comment: 7 pages, 22 figure
Monte Carlo study of the hull distribution for the q=1 Brauer model
We study a special case of the Brauer model in which every path of the model
has weight q=1. The model has been studied before as a solvable lattice model
and can be viewed as a Lorentz lattice gas. The paths of the model are also
called self-avoiding trails. We consider the model in a triangle with boundary
conditions such that one of the trails must cross the triangle from a corner to
the opposite side. Motivated by similarities between this model, SLE(6) and
critical percolation, we investigate the distribution of the hull generated by
this trail (the set of points on or surrounded by the trail) up to the hitting
time of the side of the triangle opposite the starting point. Our Monte Carlo
results are consistent with the hypothesis that for system size tending to
infinity, the hull distribution is the same as that of a Brownian motion with
perpendicular reflection on the boundary.Comment: 21 pages, 9 figure
Large fluctuations in stochastic population dynamics: momentum space calculations
Momentum-space representation renders an interesting perspective to theory of
large fluctuations in populations undergoing Markovian stochastic gain-loss
processes. This representation is obtained when the master equation for the
probability distribution of the population size is transformed into an
evolution equation for the probability generating function. Spectral
decomposition then brings about an eigenvalue problem for a non-Hermitian
linear differential operator. The ground-state eigenmode encodes the stationary
distribution of the population size. For long-lived metastable populations
which exhibit extinction or escape to another metastable state, the
quasi-stationary distribution and the mean time to extinction or escape are
encoded by the eigenmode and eigenvalue of the lowest excited state. If the
average population size in the stationary or quasi-stationary state is large,
the corresponding eigenvalue problem can be solved via WKB approximation
amended by other asymptotic methods. We illustrate these ideas in several model
examples.Comment: 20 pages, 9 figures, to appear in JSTA
Nonrelativistic Chern-Simons Vortices on the Torus
A classification of all periodic self-dual static vortex solutions of the
Jackiw-Pi model is given. Physically acceptable solutions of the Liouville
equation are related to a class of functions which we term
Omega-quasi-elliptic. This class includes, in particular, the elliptic
functions and also contains a function previously investigated by Olesen. Some
examples of solutions are studied numerically and we point out a peculiar
phenomenon of lost vortex charge in the limit where the period lengths tend to
infinity, that is, in the planar limit.Comment: 25 pages, 2+3 figures; improved exposition, corrected typos, added
one referenc
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