On the spin-statistics connection in curved spacetimes

The connection between spin and statistics is examined in the context of locally covariant quantum field theory. A generalization is proposed in which locally covariant theories are defined as functors from a category of framed spacetimes to a category of $*$-algebras. This allows for a more operational description of theories with spin, and for the derivation of a more general version of the spin-statistics connection in curved spacetimes than previously available. The proof involves a "rigidity argument" that is also applied in the standard setting of locally covariant quantum field theory to show how properties such as Einstein causality can be transferred from Minkowski spacetime to general curved spacetimes.Comment: 17pp. Contribution to the proceedings of the conference "Quantum Mathematical Physics" (Regensburg, October 2014

On the spin-statistics connection in curved spacetimes

The connection between spin and statistics is examined in the context of locally covariant quantum field theory. A generalization is proposed in which locally covariant theories are defined as functors from a category of framed spacetimes to a category of ∗-algebras. This allows for a more operational description of theories with spin, and for the derivation of a more general version of the spin-statistics connection in curved spacetimes than previously available. The proof involves a "rigidity argument" that is also applied in the standard setting of locally covariant quantum field theory to show how properties such as Einstein causality can be transferred from Minkowski spacetime to general curved spacetimes

Optimizing Mixing in Pervasive Networks: A Graph-Theoretic Perspective

One major concern in pervasive wireless applications is location privacy, where malicious eavesdroppers, based on static device identifiers, can continuously track users. As a commonly adopted countermeasure to prevent such identifier-based tracking, devices regularly and simultaneously change their identifiers in special areas called mix-zones. Although mix-zones provide spatio-temporal de-correlations between old and new identifiers, pseudonym changes, depending on the position of the mix-zone, can incur a substantial cost on the network due to lost communications and additional resources such as energy. In this paper, we address this trade-off by studying the problem of determining an optimal set of mix-zones such that the degree of mixing in the network is maximized, whereas the overall network-wide mixing cost is minimized. We follow a graph-theoretic approach and model the optimal mixing problem as a novel generalization of the vertex cover problem, called the Mix Cover (MC) problem. We propose three bounded-ratio approximation algorithms for the MC problem and validate them by an empirical evaluation of their performance on real data. The combinatorics-based approach followed here enables us to study the feasibility of determining optimal mix-zones regularly and under dynamic network conditions

Dynamical locality and covariance: What makes a physical theory the same in all spacetimes?

The question of what it means for a theory to describe the same physics on all spacetimes (SPASs) is discussed. As there may be many answers to this question, we isolate a necessary condition, the SPASs property, that should be satisfied by any reasonable notion of SPASs. This requires that if two theories conform to a common notion of SPASs, with one a subtheory of the other, and are isomorphic in some particular spacetime, then they should be isomorphic in all globally hyperbolic spacetimes (of given dimension). The SPASs property is formulated in a functorial setting broad enough to describe general physical theories describing processes in spacetime, subject to very minimal assumptions. By explicit constructions, the full class of locally covariant theories is shown not to satisfy the SPASs property, establishing that there is no notion of SPASs encompassing all such theories. It is also shown that all locally covariant theories obeying the time-slice property possess two local substructures, one kinematical (obtained directly from the functorial structure) and the other dynamical (obtained from a natural form of dynamics, termed relative Cauchy evolution). The covariance properties of relative Cauchy evolution and the kinematic and dynamical substructures are analyzed in detail. Calling local covariant theories dynamically local if their kinematical and dynamical local substructures coincide, it is shown that the class of dynamically local theories fulfills the SPASs property. As an application in quantum field theory, we give a model independent proof of the impossibility of making a covariant choice of preferred state in all spacetimes, for theories obeying dynamical locality together with typical assumptions.Comment: 60 pages, LaTeX. Version to appear in Annales Henri Poincar

Densidade, tamanho e distribuição estomática em 35 espécies de árvores na Amazônia Central

Stomata are turgor-operated valves that control water loss and CO2 uptake during photosynthesis, and thereby water relation and plant biomass accumulation is closely related to stomatal functioning. The aims of this work were to document how stomata are distributed on the leaf surface and to determine if there is any significant variation in stomatal characteristics among Amazonian tree species, and finally to study the relationship between stomatal density (S D) and tree height. Thirty five trees (>17 m tall) of different species were selected. Stomatal type, density (S D), size (S S) and stomatal distribution on the leaf surface were determined using nail polish imprints taken from both leaf surfaces. Irrespective of tree species, stomata were located only on the abaxial surface (hypostomaty), with large variation in both S D and S S among species. S D ranged from 110 mm-2 in Neea altissima to 846 mm-2 in Qualea acuminata. However, in most species S D ranges between 271 and 543 mm-2, with a negative relationship between S D and S S. We also found a positive relationship between S D and tree height (r² = 0.14, p 17 m de altura) de diferentes espécies foram selecionadas. Tipo de complexo estomático, S D, tamanho (S S) e distribuição na superfície foliar foram determinados utilizando impressões de ambas as superfícies foliares com esmalte incolor. Independente da espécie, os estômatos foram encontrados apenas na superfície abaxial (hipoestomatia) com ampla variação na S D e no S S entre espécies. A densidade estomática variou de 110 mm-2 em Neea altissima a 846 mm-2 em Qualea acuminata. Entretanto, a maioria das espécies apresentou S D entre 271 e 543 mm-2, com uma relação negativa entre S D e S S. Observou-se uma relação positiva entre S D e altura arbórea (r² = 0.14, p < 0.01), não havendo relação entre S D e espessura foliar. Os tipos estomáticos mais comuns foram: anomocíticos (37%), seguidos de paracíticos (26%) e anisocíticos (11%). Concluiu-se que em espécies da Amazônia, a distribuição de estômatos na superfície foliar está mais relacionada a fatores genéticos de cada espécie do que a variações ambientais. Entretanto, S D é fortemente influenciada por fatores ambientais concernentes à altura da árvore