Semidirect product of CCR and CAR algebras and asymptotic states in quantum electrodynamics

A C*-algebra containing the CCR and CAR algebras as its subalgebras and naturally described as the semidirect product of these algebras is discussed. A particular example of this structure is considered as a model for the algebra of asymptotic fields in quantum electrodynamics, in which Gauss' law is respected. The appearence in this algebra of a phase variable related to electromagnetic potential leads to the universal charge quantization. Translationally covariant representations of this algebra with energy-momentum spectrum in the future lightcone are investigated. It is shown that vacuum representations are necessarily nonregular with respect to total electromagnetic field. However, a class of translationally covariant, irreducible representations is constructed excplicitly, which remain as close as possible to the vacuum, but are regular at the same time. The spectrum of energy-momentum fills the whole future lightcone, but there are no vectors with energy-momentum lying on a mass hyperboloid or in the origin.Comment: 42 pages, LaTeX; minor corrections, a reference adde

The Constitutionalization of the UN Security System

The considerable activism displayed by the Security Council over the last years and its dynamic application of the powers under Chapter VII of the UN Charter recently have inspired concern for the institutional balance within the United Nations and the quest for justiciable restraints upon the Council. Such concern underlines a constitutional approach to the United Nations framework: the Charter is conceived as a kind of constitution for the community of states with the International Court of Justice as the ultimate guardian of its legality vis-a-vis the Council. Such a constitutional approach should be viewed with caution. The scrutiny of mandatory Council resolutions by the International Court of Justice must be confined to legal defects that release Member States from compliance; that is, to defects that render the resolution null and void. Such a qualification by the Court, always declaratory in character, is justified only when the Council has manifestly exceeded its powers under the Charter or violated peremptory norms of public international law

Is Einstein's equivalence principle valid for a quantum particle?

Einstein's equivalence principle in classical physics is a rule stating that the effect of gravitation is locally equivalent to the acceleration of an observer. The principle determines the motion of test particles uniquely (modulo very broad general assumptions). We show that the same principle applied to a quantum particle described by a wave function on a Newtonian gravitational background determines its motion with a similar degree of uniqueness

Population Structure of Guppies in North-Eastern Venezuela, the Area of Putative Incipient Speciation

Background Geographic barriers to gene flow and divergence among populations in sexual traits are two important causes of genetic isolation which may lead to speciation. Genetic isolation may be facilitated if these two mechanisms act synergistically. The guppy from the Cumaná region (within the Cariaco drainage) of eastern Venezuela has been previously described as a case of incipient speciation driven by sexual selection, significantly differentiated in sexual colouration and body shape from the common guppy, Poecilia reticulata. The latter occurs widely in northern Venezuela, including the south-eastern side of Cordillera de la Costa, where it inhabits streams belonging to the San Juan drainage. Here, we present molecular and morphological analyses of differentiation among guppy populations in the Cariaco and San Juan drainages. Our analyses are based on a 953 bp long mtDNA fragment, a set of 15 microsatellites (519 fish from 20 populations), and four phenotypic traits. Results Both microsatellite and mtDNA data showed that guppies inhabiting the two drainages are characterised by a significant genetic differentiation, but a higher proportion of the genetic variance was distributed among populations within regions. Most guppies in the Cariaco drainage had mtDNA from a distinct lineage, but we also found evidence for widespread introgression of mtDNA from the San Juan drainage into the Cariaco drainage. Phenotypically, populations in the two regions differed significantly only in the number of black crescents. Phenotypic clustering did not support existence of two distinct groupings, but indicated a degree of distinctiveness of Central Cumaná (CC) population. However, CC population showed little differentiation at the neutral markers from the proximate populations within the Cariaco drainage. Conclusions Our findings are consistent with only partial genetic isolation between the two geographic regions and indicate that the geographic barrier of Cordillera de la Costa has not played an important role in strengthening the incomplete pre-zygotic reproductive barrier between Cumaná and common guppy. Significant phenotypic differentiation between genetically similar (in terms of neutral variation) populations suggests that mate choice can maintain divergence at sexually selected traits despite gene flow. However, neither genetic nor phenotypic clustering supported delineation of two species within the region

Equilibrium asset pricing with transaction costs

We study risk-sharing economies where heterogeneous agents trade subject to quadratic transaction costs. The corresponding equilibrium asset prices and trading strategies are characterised by a system of nonlinear, fully coupled forward–backward stochastic differential equations. We show that a unique solution exists provided that the agents’ preferences are sufficiently similar. In a benchmark specification with linear state dynamics, the empirically observed illiquidity discounts and liquidity premia correspond to a positive relationship between transaction costs and volatility

Does Quantum Mechanics Clash with the Equivalence Principle - and Does it Matter?

With an eye on developing a quantum theory of gravity, many physicists have recently searched for quantum challenges to the equivalence principle of general relativity. However, as historians and philosophers of science are well aware, the principle of equivalence is not so clear. When clarified, we think quantum tests of the equivalence principle won't yield much. The problem is that the clash/not-clash is either already evident or guaranteed not to exist. Nonetheless, this work does help teach us what it means for a theory to be geometric.Comment: 12 page

Cognitive behavioral therapy for insomnia comorbid with COPD is feasible with preliminary evidence of positive sleep and fatigue effects

Background: Many people with COPD report difficulties falling asleep or staying asleep, insufficient sleep duration, or nonrestorative sleep. Cognitive behavioral therapy for insomnia (CBT-I) has proved effective not only in people with primary insomnia but also in people with insomnia comorbid with psychiatric and medical illness (eg, depression, cancer, and chronic pain). However, CBT-I has rarely been tested in those with COPD who have disease-related features that interfere with sleep and may lessen the effectiveness of such therapies. The purpose of this study was to determine the feasibility of applying a CBT-I intervention for people with COPD and to assess the impact of CBT-I on insomnia severity and sleep-related outcomes, fatigue, mood, and daytime functioning. Methods: The study had two phases. In Phase 1, a 6-weekly session CBT-I intervention protocol in participants with COPD was assessed to examine feasibility and acceptability. Phase 2 was a small trial utilizing a prospective two-group pre- and post-test design with random assignment to the six-session CBT-I or a six-session wellness education (WE) program to determine the effects of each intervention, with both interventions being provided by a nurse behavioral sleep medicine specialist. Results: Fourteen participants (five in Phase 1 and nine in Phase 2) completed six sessions of CBT-I and nine participants completed six sessions of WE. Participants indicated that both interventions were acceptable. Significant positive treatment-related effects of the CBT-I intervention were noted for insomnia severity (P = 0.000), global sleep quality (P = 0.002), wake after sleep onset (P = 0.03), sleep efficiency (P = 0.02), fatigue (P = 0.005), and beliefs and attitudes about sleep (P = 0.000). Significant positive effects were noted for depressed mood after WE (P = 0.005). Conclusion: Results suggest that using CBT-I in COPD is feasible and the outcomes compare favorably with those obtained in older adults with insomnia in the context of other chronic illnesses

Gravitomagnetic Moments and Dynamics of Dirac's (spin 1/2) fermions in flat space-time Maxwellian Gravity

The gravitational effects in the relativistic quantum mechanics are investigated in a relativistically derived version of Heaviside's speculative Gravity (in flat space-time) named here as Maxwellian Gravity. The standard Dirac's approach to the intrinsic spin in the fields of Maxwellian Gravity yields the gravitomagnetic moment of a Dirac (spin 1/2) particle exactly equals to its intrinsic spin. Violation of The Equivalence Principle (both at classical and quantum mechanical level) in the relativistic domain has also been reported in this work.Comment: 27 page

Continuous Spectrum of Automorphism Groups and the Infraparticle Problem

This paper presents a general framework for a refined spectral analysis of a group of isometries acting on a Banach space, which extends the spectral theory of Arveson. The concept of continuous Arveson spectrum is introduced and the corresponding spectral subspace is defined. The absolutely continuous and singular-continuous parts of this spectrum are specified. Conditions are given, in terms of the transposed action of the group of isometries, which guarantee that the pure-point and continuous subspaces span the entire Banach space. In the case of a unitarily implemented group of automorphisms, acting on a $C^*$-algebra, relations between the continuous spectrum of the automorphisms and the spectrum of the implementing group of unitaries are found. The group of spacetime translation automorphisms in quantum field theory is analyzed in detail. In particular, it is shown that the structure of its continuous spectrum is relevant to the problem of existence of (infra-)particles in a given theory.Comment: 31 pages, LaTeX. As appeared in Communications in Mathematical Physic