14,137 research outputs found
Gauge invariance of massless QED
A simple general proof of gauge invariance in QED is given in the framework
of causal perturbation theory. It illustrates a method which can also be used
in non-abelian gauge theories.Comment: 7 pages, TEX-file, Zuerich University Preprint ZU-TH-33/199
Dipole matrix elements in helium in the first order shielding approximation
First order shielding approximation used to calculate off-diagonal matrix elements of dipole moment operator for heliu
General massive gauge theory
The concept of perturbative gauge invariance formulated exclusively by means
of asymptotic fields is used to construct massive gauge theories. We consider
the interactions of massive and massless gauge fields together with
fermionic ghost and anti-ghost fields. First order gauge invariance
requires the introduction of unphysical scalars (Goldstone bosons) and fixes
their trilinear couplings. At second order additional physical scalars (Higgs
fields) are necessary, their coupling is further restricted at third order. In
case of one physical scalar all couplings are determined by gauge invariance,
including the Higgs potential. For three massive and one massless gauge field
the electroweak theory comes out as the unique solution.Comment: 20 pages, latex, no figure
EPG-representations with small grid-size
In an EPG-representation of a graph each vertex is represented by a path
in the rectangular grid, and is an edge in if and only if the paths
representing an share a grid-edge. Requiring paths representing edges
to be x-monotone or, even stronger, both x- and y-monotone gives rise to three
natural variants of EPG-representations, one where edges have no monotonicity
requirements and two with the aforementioned monotonicity requirements. The
focus of this paper is understanding how small a grid can be achieved for such
EPG-representations with respect to various graph parameters.
We show that there are -edge graphs that require a grid of area
in any variant of EPG-representations. Similarly there are
pathwidth- graphs that require height and area in
any variant of EPG-representations. We prove a matching upper bound of
area for all pathwidth- graphs in the strongest model, the one where edges
are required to be both x- and y-monotone. Thus in this strongest model, the
result implies, for example, , and area bounds
for bounded pathwidth graphs, bounded treewidth graphs and all classes of
graphs that exclude a fixed minor, respectively. For the model with no
restrictions on the monotonicity of the edges, stronger results can be achieved
for some graph classes, for example an area bound for bounded treewidth
graphs and bound for graphs of bounded genus.Comment: Appears in the Proceedings of the 25th International Symposium on
Graph Drawing and Network Visualization (GD 2017
On Gauge Invariance and Spontaneous Symmetry Breaking
We show how the widely used concept of spontaneous symmetry breaking can be
explained in causal perturbation theory by introducing a perturbative version
of quantum gauge invariance. Perturbative gauge invariance, formulated
exclusively by means of asymptotic fields, is discussed for the simple example
of Abelian U(1) gauge theory (Abelian Higgs model). Our findings are relevant
for the electroweak theory, as pointed out elsewhere.Comment: 13 pages, latex, no figure
Slow update of internal representations impedes synchronization in autism
Autism is a neurodevelopmental disorder characterized by impaired social skills, motor and perceptual atypicalities. These difficulties were explained within the Bayesian framework as either reflecting oversensitivity to prediction errors or – just the opposite – slow updating of such errors. To test these opposing theories, we administer paced finger-tapping, a synchronization task that requires use of recent sensory information for fast error-correction. We use computational modelling to disentangle the contributions of error-correction from that of noise in keeping temporal intervals, and in executing motor responses. To assess the specificity of tapping characteristics to autism, we compare performance to both neurotypical individuals and individuals with dyslexia. Only the autism group shows poor sensorimotor synchronization. Trial-by-trial modelling reveals typical noise levels in interval representations and motor responses. However, rate of error correction is reduced in autism, impeding synchronization ability. These results provide evidence for slow updating of internal representations in autism
Aperiodic invariant continua for surface homeomorphisms
We prove that if a homeomorphism of a closed orientable surface S has no
wandering points and leaves invariant a compact, connected set K which contains
no periodic points, then either K=S and S is a torus, or is the
intersection of a decreasing sequence of annuli. A version for non-orientable
surfaces is given.Comment: 8 pages, to appear in Mathematische Zeitschrif
Self-replication and splitting of domain patterns in reaction-diffusion systems with fast inhibitor
An asymptotic equation of motion for the pattern interface in the
domain-forming reaction-diffusion systems is derived. The free boundary problem
is reduced to the universal equation of non-local contour dynamics in two
dimensions in the parameter region where a pattern is not far from the points
of the transverse instabilities of its walls. The contour dynamics is studied
numerically for the reaction-diffusion system of the FitzHugh-Nagumo type. It
is shown that in the asymptotic limit the transverse instability of the
localized domains leads to their splitting and formation of the multidomain
pattern rather than fingering and formation of the labyrinthine pattern.Comment: 9 pages (ReVTeX), 5 figures (postscript). To be published in Phys.
Rev.
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