184 research outputs found
Duality Invariant Actions and Generalised Geometry
We construct the non-linear realisation of the semi-direct product of E(11)
and its first fundamental representation at lowest order and appropriate to
spacetime dimensions four to seven. This leads to a non-linear realisation of
the duality groups and introduces fields that depend on a generalised space
which possess a generalised vielbein. We focus on the part of the generalised
space on which the duality groups alone act and construct an invariant action.Comment: 59 pages (typos fixed and added comments
Quantum-Classical Correspondence of Dynamical Observables, Quantization and the Time of Arrival Correspondence Problem
We raise the problem of constructing quantum observables that have classical
counterparts without quantization. Specifically we seek to define and motivate
a solution to the quantum-classical correspondence problem independent from
quantization and discuss the general insufficiency of prescriptive
quantization, particularly the Weyl quantization. We demonstrate our points by
constructing time of arrival operators without quantization and from these
recover their classical counterparts
Information-theoretic postulates for quantum theory
Why are the laws of physics formulated in terms of complex Hilbert spaces?
Are there natural and consistent modifications of quantum theory that could be
tested experimentally? This book chapter gives a self-contained and accessible
summary of our paper [New J. Phys. 13, 063001, 2011] addressing these
questions, presenting the main ideas, but dropping many technical details. We
show that the formalism of quantum theory can be reconstructed from four
natural postulates, which do not refer to the mathematical formalism, but only
to the information-theoretic content of the physical theory. Our starting point
is to assume that there exist physical events (such as measurement outcomes)
that happen probabilistically, yielding the mathematical framework of "convex
state spaces". Then, quantum theory can be reconstructed by assuming that (i)
global states are determined by correlations between local measurements, (ii)
systems that carry the same amount of information have equivalent state spaces,
(iii) reversible time evolution can map every pure state to every other, and
(iv) positivity of probabilities is the only restriction on the possible
measurements.Comment: 17 pages, 3 figures. v3: some typos corrected and references updated.
Summarizes the argumentation and results of arXiv:1004.1483. Contribution to
the book "Quantum Theory: Informational Foundations and Foils", Springer
Verlag (http://www.springer.com/us/book/9789401773027), 201
Rotating Higher Spin Partition Functions and Extended BMS Symmetries
We evaluate one-loop partition functions of higher-spin fields in thermal
flat space with angular potentials; this computation is performed in arbitrary
space-time dimension, and the result is a simple combination of Poincar\'e
characters. We then focus on dimension three, showing that suitable products of
one-loop partition functions coincide with vacuum characters of higher-spin
asymptotic symmetry algebras at null infinity. These are extensions of the
bms_3 algebra that emerges in pure gravity, and we propose a way to build their
unitary representations and to compute the associated characters. We also
extend our investigations to supergravity and to a class of gauge theories
involving higher-spin fermionic fields.Comment: 58 pages; clarifications and references added; version to be
published in JHE
Continuity properties of measurable group cohomology
A version of group cohomology for locally compact groups and Polish modules
has previously been developed using a bar resolution restricted to measurable
cochains. That theory was shown to enjoy analogs of most of the standard
algebraic properties of group cohomology, but various analytic features of
those cohomology groups were only partially understood.
This paper re-examines some of those issues. At its heart is a simple
dimension-shifting argument which enables one to `regularize' measurable
cocycles, leading to some simplifications in the description of the cohomology
groups. A range of consequences are then derived from this argument.
First, we prove that for target modules that are Fr\'echet spaces, the
cohomology groups agree with those defined using continuous cocycles, and hence
they vanish in positive degrees when the acting group is compact. Using this,
we then show that for Fr\'echet, discrete or toral modules the cohomology
groups are continuous under forming inverse limits of compact base groups, and
also under forming direct limits of discrete target modules.
Lastly, these results together enable us to establish various circumstances
under which the measurable-cochains cohomology groups coincide with others
defined using sheaves on a semi-simplicial space associated to the underlying
group, or sheaves on a classifying space for that group. We also prove in some
cases that the natural quotient topologies on the measurable-cochains
cohomology groups are Hausdorff.Comment: 52 pages. [Nov 22, 2011:] Major re-write with Calvin C. Moore as new
co-author. Results from previous version strengthened and several new results
added. [Nov 25, 2012:] Final version now available at springerlink.co
What is Quantum? Unifying Its Micro-Physical and Structural Appearance
We can recognize two modes in which 'quantum appears' in macro domains: (i) a
'micro-physical appearance', where quantum laws are assumed to be universal and
they are transferred from the micro to the macro level if suitable 'quantum
coherence' conditions (e.g., very low temperatures) are realized, (ii) a
'structural appearance', where no hypothesis is made on the validity of quantum
laws at a micro level, while genuine quantum aspects are detected at a
structural-modeling level. In this paper, we inquire into the connections
between the two appearances. We put forward the explanatory hypothesis that,
'the appearance of quantum in both cases' is due to 'the existence of a
specific form of organisation, which has the capacity to cope with random
perturbations that would destroy this organisation when not coped with'. We
analyse how 'organisation of matter', 'organisation of life', and 'organisation
of culture', play this role each in their specific domain of application, point
out the importance of evolution in this respect, and put forward how our
analysis sheds new light on 'what quantum is'.Comment: 10 page
Pseudo-differential operators associated to general type I locally compact groups
In a recent paper by M. Mantoiu and M. Ruzhansky, a global
pseudo-differential calculus has been developed for unimodular groups of type
I. In the present article we generalize the main results to arbitrary locally
compact groups of type I. Our methods involve the use of Plancherel's theorem
for non-unimodular groups. We also make connections with a -algebraic
formalism, involving dynamical systems, and give explicit constructions for the
group of affine transformations of the real line.Comment: 21 page
Quantized reduction as a tensor product
Symplectic reduction is reinterpreted as the composition of arrows in the
category of integrable Poisson manifolds, whose arrows are isomorphism classes
of dual pairs, with symplectic groupoids as units. Morita equivalence of
Poisson manifolds amounts to isomorphism of objects in this category.
This description paves the way for the quantization of the classical
reduction procedure, which is based on the formal analogy between dual pairs of
Poisson manifolds and Hilbert bimodules over C*-algebras, as well as with
correspondences between von Neumann algebras. Further analogies are drawn with
categories of groupoids (of algebraic, measured, Lie, and symplectic type). In
all cases, the arrows are isomorphism classes of appropriate bimodules, and
their composition may be seen as a tensor product. Hence in suitable categories
reduction is simply composition of arrows, and Morita equivalence is
isomorphism of objects.Comment: 44 pages, categorical interpretation adde
Identification and functional characterisation of CRK12:CYC9, a novel cyclin-dependent kinase (CDK)-cyclin complex in Trypanosoma brucei
The protozoan parasite, Trypanosoma brucei, is spread by the tsetse fly and causes trypanosomiasis in humans and animals. Both the life cycle and cell cycle of the parasite are complex. Trypanosomes have eleven cdc2-related kinases (CRKs) and ten cyclins, an unusually large number for a single celled organism. To date, relatively little is known about the function of many of the CRKs and cyclins, and only CRK3 has previously been shown to be cyclin-dependent in vivo. Here we report the identification of a previously uncharacterised CRK:cyclin complex between CRK12 and the putative transcriptional cyclin, CYC9. CRK12:CYC9 interact to form an active protein kinase complex in procyclic and bloodstream T. brucei. Both CRK12 and CYC9 are essential for the proliferation of bloodstream trypanosomes in vitro, and we show that CRK12 is also essential for survival of T. brucei in a mouse model, providing genetic validation of CRK12:CYC9 as a novel drug target for trypanosomiasis. Further, functional characterisation of CRK12 and CYC9 using RNA interference reveals roles for these proteins in endocytosis and cytokinesis, respectively
Planet Populations as a Function of Stellar Properties
Exoplanets around different types of stars provide a window into the diverse
environments in which planets form. This chapter describes the observed
relations between exoplanet populations and stellar properties and how they
connect to planet formation in protoplanetary disks. Giant planets occur more
frequently around more metal-rich and more massive stars. These findings
support the core accretion theory of planet formation, in which the cores of
giant planets form more rapidly in more metal-rich and more massive
protoplanetary disks. Smaller planets, those with sizes roughly between Earth
and Neptune, exhibit different scaling relations with stellar properties. These
planets are found around stars with a wide range of metallicities and occur
more frequently around lower mass stars. This indicates that planet formation
takes place in a wide range of environments, yet it is not clear why planets
form more efficiently around low mass stars. Going forward, exoplanet surveys
targeting M dwarfs will characterize the exoplanet population around the lowest
mass stars. In combination with ongoing stellar characterization, this will
help us understand the formation of planets in a large range of environments.Comment: Accepted for Publication in the Handbook of Exoplanet
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