116 research outputs found
Foliations and Chern-Heinz inequalities
We extend the Chern-Heinz inequalities about mean curvature and scalar
curvature of graphs of -functions to leaves of transversally oriented
codimension one -foliations of Riemannian manifolds. That extends
partially Salavessa's work on mean curvature of graphs and generalize results
of Barbosa-Kenmotsu-Oshikiri \cite{barbosa-kenmotsu-Oshikiri} and
Barbosa-Gomes-Silveira \cite{barbosa-gomes-silveira} about foliations of
3-dimensional Riemannian manifolds by constant mean curvature surfaces. These
Chern-Heinz inequalities for foliations can be applied to prove
Haymann-Makai-Osserman inequality (lower bounds of the fundamental tones of
bounded open subsets in terms of its inradius)
for embedded tubular neighborhoods of simple curves of .Comment: This paper is an improvment of an earlier paper titled On Chern-Heinz
Inequalities. 8 Pages, Late
On the problem of mass-dependence of the two-point function of the real scalar free massive field on the light cone
We investigate the generally assumed inconsistency in light cone quantum
field theory that the restriction of a massive, real, scalar, free field to the
nullplane is independent of mass \cite{LKS}, but the
restriction of the two-point function depends on it (see, e.g., \cite{NakYam77,
Yam97}). We resolve this inconsistency by showing that the two-point function
has no canonical restriction to in the sense of distribution theory.
Only the so-called tame restriction of the two-point function exists which we
have introduced in \cite{Ull04sub}. Furthermore, we show that this tame
restriction is indeed independent of mass. Hence the inconsistency appears only
by the erroneous assumption that the two-point function would have a
(canonical) restriction to .Comment: 10 pages, 2 figure
Fermion mixing in quasi-free states
Quantum field theoretic treatments of fermion oscillations are typically
restricted to calculations in Fock space. In this letter we extend the
oscillation formulae to include more general quasi-free states, and also
consider the case when the mixing is not unitary.Comment: 10 pages, Plain Te
Wavefront sets and polarizations on supermanifolds
In this paper we develop the foundations for microlocal analysis on supermanifolds. Making use of pseudodifferential operators on supermanifolds as introduced by Rempel and Schmitt, we define a suitable notion of super wavefront set for superdistributions which generalizes Dencker's polarization sets for vector-valued distributions to supergeometry. In particular, our super wavefront sets detect polarization information of the singularities of superdistributions. We prove a refined pullback theorem for superdistributions along supermanifold morphisms, which as a special case establishes criteria when two superdistributions may be multiplied. As an application of our framework, we study the singularities of distributional solutions of a supersymmetric field theory
Polynomial-sized Semidefinite Representations of Derivative Relaxations of Spectrahedral Cones
We give explicit polynomial-sized (in and ) semidefinite
representations of the hyperbolicity cones associated with the elementary
symmetric polynomials of degree in variables. These convex cones form a
family of non-polyhedral outer approximations of the non-negative orthant that
preserve low-dimensional faces while successively discarding high-dimensional
faces. More generally we construct explicit semidefinite representations
(polynomial-sized in , and ) of the hyperbolicity cones associated with
th directional derivatives of polynomials of the form where the are symmetric
matrices. These convex cones form an analogous family of outer approximations
to any spectrahedral cone. Our representations allow us to use semidefinite
programming to solve the linear cone programs associated with these convex
cones as well as their (less well understood) dual cones.Comment: 20 pages, 1 figure. Minor changes, expanded proof of Lemma
Vacuum Structures in Hamiltonian Light-Front Dynamics
Hamiltonian light-front dynamics of quantum fields may provide a useful
approach to systematic non-perturbative approximations to quantum field
theories. We investigate inequivalent Hilbert-space representations of the
light-front field algebra in which the stability group of the light-front is
implemented by unitary transformations. The Hilbert space representation of
states is generated by the operator algebra from the vacuum state. There is a
large class of vacuum states besides the Fock vacuum which meet all the
invariance requirements. The light-front Hamiltonian must annihilate the vacuum
and have a positive spectrum. We exhibit relations of the Hamiltonian to the
nontrivial vacuum structure.Comment: 16 pages, report \# ANL-PHY-7524-TH-93, (Latex
Training American listeners to perceive Mandarin tones
This is the publisher's version, also available electronically from http://scitation.aip.org/content/asa/journal/jasa/106/6/10.1121/1.428217.Auditory training has been shown to be effective in the identification of non-native segmental distinctions. In this study, it was investigated whether such training is applicable to the acquisition of non-native suprasegmentalcontrasts, i.e., Mandarin tones. Using the high-variability paradigm, eight American learners of Mandarin were trained in eight sessions during the course of two weeks to identify the four tones in natural words produced by native Mandarin talkers. The traineesâ identification accuracy revealed an average 21% increase from the pretest to the post-test, and the improvement gained in training was generalized to new stimuli (18% increase) and to new talkers and stimuli (25% increase). Moreover, the six-month retention test showed that the improvement was retained long after training by an average 21% increase from the pretest. The results are discussed in terms of non-native suprasegmental perceptual modification, and the analogies between L2 acquisition processes at the segmental and suprasegmental levels
Galilei-invariant equations for massive fields
Galilei-invariant equations for massive fields with various spins have been
found and classified. They have been derived directly, i.e., by using
requirement of the Galilei invariance and various facts on representations of
the Galilei group deduced in the paper written by de Montigny M, Niederle J and
Nikitin A G, J. Phys. A \textbf{39}, 1-21, 2006. A completed list of
non-equivalent Galilei-invariant wave equations for vector and scalar fields is
presented. It shows two things. First that the collection of such equations is
very broad and describes many physically consistent systems. In particular it
is possible to describe spin-orbit and Darwin couplings in frames of
Galilei-invariant approach. Second, these Galilei-invariant equations can be
obtained either via contraction of known relativistic equations or via
contractions of quite new relativistic wave equations.Comment: Minor improvements of the text has been made and misprints are
correcte
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