10,821 research outputs found
An Algebraic Spin and Statistics Theorem
A spin-statistics theorem and a PCT theorem are obtained in the context of
the superselection sectors in Quantum Field Theory on a 4-dimensional
space-time. Our main assumption is the requirement that the modular groups of
the von Neumann algebras of local observables associated with wedge regions act
geometrically as pure Lorentz transformations. Such a property, satisfied by
the local algebras generated by Wightman fields because of the
Bisognano-Wichmann theorem, is regarded as a natural primitive assumption.Comment: 15 pages, plain TeX, an error in the statement of a theorem has been
corrected, to appear in Commun. Math. Phy
Multiple testing for SNP-SNP interactions
Most genetic diseases are complex, i.e. associated to combinations of SNPs rather than individual SNPs. In the last few years, this topic has often been addressed in terms of SNP-SNP interaction patterns given as expressions linked by logical operators. Methods for multiple testing in high-dimensional settings can be applied when many SNPs are considered simultaneously. However, another less well-known multiple testing problem arises within a fixed subset of SNPs when the logic expression is chosen optimally. In this article, we propose a general asymptotic approach for deriving the distribution of the maximally selected chi-square statistic in various situations. We show how this result can be used for testing logic expressions - in particular SNP-SNP interaction patterns - while controlling for multiple comparisons. Simulations show that our method provides multiple testing adjustment when the logic expression is chosen such as to maximize the statistic. Its benefit is demonstrated through an application to a real
dataset from a large population-based study considering allergy and asthma in KORA. An implementation of our method is available from the Comprehensive R Archive Network (CRAN) as R package 'SNPmaxsel'
A New Approach to Spin and Statistics
We give an algebraic proof of the spin-statistics connection for the
parabosonic and parafermionic quantum topological charges of a theory of local
observables with a modular PCT-symmetry. The argument avoids the use of the
spinor calculus and also works in 1+2 dimensions. It is expected to be a
progress towards a general spin-statistics theorem including also
(1+2)-dimensional theories with braid group statistics.Comment: LATEX, 15 pages, no figure
Modelling linguistic taxonomic dynamics
This paper presents the results of the application of a bit-string model of
languages (Schulze and Stauffer 2005) to problems of taxonomic patterns. The
questions addressed include the following: (1) Which parameters are minimally
ne eded for the development of a taxonomic dynamics leading to the type of
distribution of language family sizes currently attested (as measured in the i
number of languages per family), which appears to be a power-law? (2) How may
such a model be coupled with one of the dynamics of speaker populations leading
to the type of language size seen today, which appears to follow a log-normal
distribution?Comment: 18 pages including 9 figure
Using a Combination of Micro-Computed Tomography, CAD and 3D Printing Techniques to Reconstruct Incomplete 19th-Century Cantonese Chess Pieces
An Algebraic Jost-Schroer Theorem for Massive Theories
We consider a purely massive local relativistic quantum theory specified by a
family of von Neumann algebras indexed by the space-time regions. We assume
that, affiliated with the algebras associated to wedge regions, there are
operators which create only single particle states from the vacuum (so-called
polarization-free generators) and are well-behaved under the space-time
translations. Strengthening a result of Borchers, Buchholz and Schroer, we show
that then the theory is unitarily equivalent to that of a free field for the
corresponding particle type. We admit particles with any spin and localization
of the charge in space-like cones, thereby covering the case of
string-localized covariant quantum fields.Comment: 21 pages. The second (and crucial) hypothesis of the theorem has been
relaxed and clarified, thanks to the stimulus of an anonymous referee. (The
polarization-free generators associated with wedge regions, which always
exist, are assumed to be temperate.
Uniformly Accelerated Observer in Moyal Spacetime
In Minkowski space, an accelerated reference frame may be defined as one that
is related to an inertial frame by a sequence of instantaneous Lorentz
transformations. Such an accelerated observer sees a causal horizon, and the
quantum vacuum of the inertial observer appears thermal to the accelerated
observer, also known as the Unruh effect. We argue that an accelerating frame
may be similarly defined (i.e. as a sequence of instantaneous Lorentz
transformations) in noncommutative Moyal spacetime, and discuss the twisted
quantum field theory appropriate for such an accelerated observer. Our analysis
shows that there are several new features in the case of noncommutative
spacetime: chiral massless fields in dimensions have a qualitatively
different behavior compared to massive fields. In addition, the vacuum of the
inertial observer is no longer an equilibrium thermal state of the accelerating
observer, and the Bose-Einstein distribution acquires -dependent
corrections.Comment: 19 pages. Typos correcte
Birth, survival and death of languages by Monte Carlo simulation
Simulations of physicists for the competition between adult languages since
2003 are reviewed. How many languages are spoken by how many people? How many
languages are contained in various language families? How do language
similarities decay with geographical distance, and what effects do natural
boundaries have? New simulations of bilinguality are given in an appendix.Comment: 24 pages review, draft for Comm.Comput.Phys., plus appendix on
bilingualit
An algebraic Haag's theorem
Under natural conditions (such as split property and geometric modular action
of wedge algebras) it is shown that the unitary equivalence class of the net of
local (von Neumann) algebras in the vacuum sector associated to double cones
with bases on a fixed space-like hyperplane completely determines an algebraic
QFT model. More precisely, if for two models there is unitary connecting all of
these algebras, then --- without assuming that this unitary also connects their
respective vacuum states or spacetime symmetry representations --- it follows
that the two models are equivalent. This result might be viewed as an algebraic
version of the celebrated theorem of Rudolf Haag about problems regarding the
so-called "interaction-picture" in QFT.
Original motivation of the author for finding such an algebraic version came
from conformal chiral QFT. Both the chiral case as well as a related conjecture
about standard half-sided modular inclusions will be also discussed
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