Is Quantum Gravity a Chern-Simons Theory?

We propose a model of quantum gravity in arbitrary dimensions defined in terms of the BV quantization of a supersymmetric, infinite dimensional matrix model. This gives an (AKSZ-type) Chern-Simons theory with gauge algebra the space of observables of a quantum mechanical Hilbert space H. The model is motivated by previous attempts to formulate gravity in terms of non-commutative, phase space, field theories as well as the Fefferman-Graham curved analog of Dirac spaces for conformally invariant wave equations. The field equations are flat connection conditions amounting to zero curvature and parallel conditions on operators acting on H. This matrix-type model may give a better defined setting for a quantum gravity path integral. We demonstrate that its underlying physics is a summation over Hamiltonians labeled by a conformal class of metrics and thus a sum over causal structures. This gives in turn a model summing over fluctuating metrics plus a tower of additional modes-we speculate that these could yield improved UV behavior.Comment: 22 pages, LaTeX, 3 figures, references added, version to appear in PR

Hierarchical models for service-oriented systems

We present our approach to the denotation and representation of hierarchical graphs: a suitable algebra of hierarchical graphs and two domains of interpretations. Each domain of interpretation focuses on a particular perspective of the graph hierarchy: the top view (nested boxes) is based on a notion of embedded graphs while the side view (tree hierarchy) is based on gs-graphs. Our algebra can be understood as a high-level language for describing such graphical models, which are well suited for defining graphical representations of service-oriented systems where nesting (e.g. sessions, transactions, locations) and linking (e.g. shared channels, resources, names) are key aspects

Scalar Field with Robin Boundary Conditions in the Worldline Formalism

The worldline formalism has been widely used to compute physical quantities in quantum field theory. However, applications of this formalism to quantum fields in the presence of boundaries have been studied only recently. In this article we show how to compute in the worldline approach the heat kernel expansion for a scalar field with boundary conditions of Robin type. In order to describe how this mechanism works, we compute the contributions due to the boundary conditions to the coefficients A_1, A_{3/2} and A_2 of the heat kernel expansion of a scalar field on the positive real line.Comment: Presented at 8th Workshop on Quantum Field Theory Under the Influence of External Conditions (QFEXT 07), Leipzig, Germany, 16-21 Sep 200

Quantum Gravity and Causal Structures: Second Quantization of Conformal Dirac Algebras

It is postulated that quantum gravity is a sum over causal structures coupled to matter via scale evolution. Quantized causal structures can be described by studying simple matrix models where matrices are replaced by an algebra of quantum mechanical observables. In particular, previous studies constructed quantum gravity models by quantizing the moduli of Laplace, weight and defining-function operators on Fefferman-Graham ambient spaces. The algebra of these operators underlies conformal geometries. We extend those results to include fermions by taking an osp(1|2) "Dirac square root" of these algebras. The theory is a simple, Grassmann, two-matrix model. Its quantum action is a Chern-Simons theory whose differential is a first-quantized, quantum mechanical BRST operator. The theory is a basic ingredient for building fundamental theories of physical observables.Comment: 4 pages, LaTe

Effect of dispersion interactions on the properties of LiF in condensed phases

Classical molecular dynamics simulations are performed on LiF in the framework of the polarizable ion model. The overlap-repulsion and polarization terms of the interaction potential are derived on a purely non empirical, first-principles basis. For the dispersion, three cases are considered: a first one in which the dispersion parameters are set to zero and two others in which they are included, with different parameterizations. Various thermodynamic, structural and dynamic properties are calculated for the solid and liquid phases. The melting temperature is also obtained by direct coexistence simulations of the liquid and solid phases. Dispersion interactions appear to have an important effect on the density of both phases and on the melting point, although the liquid properties are not affected when simulations are performed in the NVT ensemble at the experimental density.Comment: 8 pages, 5 figure

Dwelling or duelling in possibilities: how (Ir)relevant are African feminisms?

In its four decades of rebirth, the world has debated (enough) the relevance of feminism, but there is, surprisingly, refreshingly emergent dimensions at the turn of the twenty-first century: feminisms from feminism flowing from Africa. The theories or models of Womanism, Stiwanism, Motherism, and Nego-feminism, with their underlying assumptions and values,were all born at various end times of the twentieth century with a common objective of seeking gender justice. This paper examines the crucial question of how relevant these models are to the global practice of woman as human. What propels their separateness, and why didn‘t they combine to make a more solid stance on the plight of the African woman? In fact, why can‘t they simply identify with the general feminism? Put differently, are they dwelling in the same terrain or are they separable and easily recognisable discourses duelling in possibilities for the woman in Africa in particular and the woman of the globe in general? More specifically, how (ir)relevant are African feminisms?In trying to answer these questions, the paper presents a critical review of the afore-mentioned theories of African feminisms with the goal of providing readers an understanding of what is new in each model, and what is similar or different between the various strands of African feminisms. The paper concludes with the author‘s analysis of the model that holds the best promise or possibilities for African feminism to achieve its seemingly elusive goal of gender equality

Topological invariants in interacting Quantum Spin Hall: a Cluster Perturbation Theory approach

Using Cluster Perturbation Theory we calculate Green's functions, quasi-particle energies and topological invariants for interacting electrons on a 2-D honeycomb lattice, with intrinsic spin-orbit coupling and on-site e-e interaction. This allows to define the parameter range (Hubbard U vs spin-orbit coupling) where the 2D system behaves as a trivial insulator or Quantum Spin Hall insulator. This behavior is confirmed by the existence of gapless quasi-particle states in honeycomb ribbons. We have discussed the importance of the cluster symmetry and the effects of the lack of full translation symmetry typical of CPT and of most Quantum Cluster approaches. Comments on the limits of applicability of the method are also provided.Comment: 7 pages, 7 figures: discussion improved, one figure added, references updated. Matches version published in New J. Phy

On the definition of parallel independence in the algebraic approaches to graph transformation

Parallel independence between transformation steps is a basic and well-understood notion of the algebraic approaches to graph transformation, and typically guarantees that the two steps can be applied in any order obtaining the same resulting graph, up to isomorphism. The concept has been redefined for several algebraic approaches as variations of a classical “algebraic” condition, requiring that each matching morphism factorizes through the context graphs of the other transformation step. However, looking at some classical papers on the double-pushout approach, one finds that the original definition of parallel independence was formulated in set-theoretical terms, requiring that the intersection of the images of the two left-hand sides in the host graph is contained in the intersection of the two interface graphs. The relationship between this definition and the standard algebraic one is discussed in this position paper, both in the case of left-linear and non-left-linear rules

An Algebra of Hierarchical Graphs

We define an algebraic theory of hierarchical graphs, whose axioms characterise graph isomorphism: two terms are equated exactly when they represent the same graph. Our algebra can be understood as a high-level language for describing graphs with a node-sharing, embedding structure, and it is then well suited for defining graphical representations of software models where nesting and linking are key aspects

The Silurian of Sardinia

The present volume “The Silurian of Sardinia” is composed of two related components. The first part comprises seven contributions introduced by an historical overview on the studies already carried out on the Silurian faunas of Sardinia. It aims to delineate a comprehensive scenario of the Silurian of Sardinia within a proper geological setting. A global overview regarding the palaeoenvironment and palaeogeography is also provided. The second part of the volume consists of seven research papers that illustrate actual knowledge on major fossil groups encountered in the Silurian limestones and shales of southern Sardinia