1,720,983 research outputs found
Invariant States on Noncommutative Tori
No full textFor any number h such that ħ:=h/2π is irrational and any skew-symmetric, non-degenerate bilinear form σ:Z2g×Z2g→Z, let be hg,σ be the twisted group ∗-algebra C[Z2g] and consider the ergodic group of ∗-automorphisms of hg,σ induced by the action of the symplectic group Sp(Z2g,σ). We show that the only Sp(Z2g,σ)-invariant state on hg,σ is the trace state τ
Møller operators and Hadamard states for Dirac fields with MIT boundary conditions
No full textThe aim of this paper is to prove the existence of Hadamard states for Dirac fields coupled with MIT boundary conditions on any globally hyperbolic manifold with timelike boundary once a suitable propagation of singularities theorem is assumed. To this avail, we consider particular pairs of weakly-hyperbolic symmetric systems coupled with admissible boundary conditions. We then prove the existence of an isomorphism between the solution spaces to the Cauchy problems associated with these operators – this isomorphism is in fact unitary between the spaces of L
2
-initial data. In particular, we show that for Dirac fields with MIT boundary conditions, this isomorphism can be lifted to a ∗-isomorphism between the algebras of Dirac fields and that any Hadamard state can be pulled back along this ∗-isomorphism preserving the singular structure of its two-point distribution
On boundary conditions for linearised Einstein's equations
Full text linkWe investigate the properties of a fairly large class of boundary conditions for the linearised Einstein equations in the Riemannian setting, ones which generalise the linearised counterpart of boundary conditions proposed by Anderson. Through the prism of the quest to quantise gravitational waves in curved spacetimes, we study their properties from the point of view of ellipticity, gauge invariance, and the existence of a spectral gap
Radiative observables for linearized gravity on asymptotically flat spacetimes and their boundary induced states
Full text linkWe discuss the quantization of linearized gravity on globally hyperbolic, asymptotically flat, vacuum spacetimes and the construction of distinguished states which are both of Hadamard form and invariant under the action of all bulk isometries. The procedure, we follow, consists of looking for a realization of the observables of the theory as a sub-algebra of an auxiliary, non-dynamical algebra constructed on future null infinity ℑ+. The applicability of this scheme is tantamount to proving that a solution of the equations of motion for linearized gravity can be extended smoothly to ℑ+. This has been claimed to be possible provided that a suitable gauge fixing condition, first written by Geroch and Xanthopoulos, is imposed. We review its definition critically showing that there exists a previously unnoticed obstruction in its implementation leading us to introducing the concept of radiative observables. These constitute an algebra for which a Hadamard state induced from null infinity and invariant under the action of all
spacetime isometries exists and it is explicitly constructed
Non-existence of natural states for Abelian Chern–Simons theory
Full text linkWe give an elementary proof that Abelian Chern-Simons theory, described as a functor from oriented surfaces to C*-algebras, does not admit a natural state. Non-existence of natural states is thus not only a phenomenon of quantum field theories on Lorentzian manifolds, but also of topological quantum field theories formulated in the algebraic approach
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Full text link“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
Appropriate Similarity Measures for Author Cocitation Analysis
Full text linkWe provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
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