Asymptotic structure of the Rarita-Schwinger theory in four spacetime dimensions at spatial infinity

We investigate the asymptotic structure of the free Rarita-Schwinger theory in four spacetime dimensions at spatial infinity in the Hamiltonian formalism. We impose boundary conditions for the spin-3/2 field that are invariant under an infinite-dimensional (abelian) algebra of non-trivial asymptotic fermionic symmetries. The compatibility of this set of boundary conditions with the invariance of the theory under Lorentz boosts requires the introduction of boundary degrees of freedom in the Hamiltonian action, along the lines of electromagnetism. These boundary degrees of freedom modify the symplectic structure by a surface contribution appearing in addition to the standard bulk piece. The Poincaré transformations have then well-defined (integrable, finite) canonical generators. Moreover, improper fermionic gauge symmetries, which are also well-defined canonical transformations, are further enlarged and turn out to be parametrized by two independent angle-dependent spinor functions at infinity, which lead to an infinite-dimensional fermionic algebra endowed with a central charge. We extend next the analysis to the supersymmetric spin-(1, 3/2) and spin-(2, 3/2) multiplets. First, we present the canonical realization of the super-Poincaré algebra on the spin-(1, 3/2) multiplet, which is shown to be consistently enhanced by the infinite-dimensional abelian algebra of angle-dependent bosonic and fermionic improper gauge symmetries associated with the electromagnetic and the Rarita-Schwinger fields, respectively. A similar analysis of the spin-(2, 3/2) multiplet is then carried out to obtain the canonical realization of the super-Poincaré algebra, consistently enhanced by the abelian improper bosonic gauge transformations of the spin-2 field (BMS supertranslations) and the abelian improper fermionic gauge transformations of the spin-3/2 field.

Equivalence of Models in Loop Quantum Cosmology and Group Field Theory

The paradigmatic models often used to highlight cosmological features of loop quantum gravity and group field theory are shown to be equivalent, in the sense that they are different realizations of the same model given by harmonic cosmology. The loop version of harmonic cosmology is a canonical realization, while the group-field version is a bosonic realization. The existence of a large number of bosonic realizations suggests generalizations of models in group field cosmology.

Deverbal -mine action nominals in the Estonian dialect corpus

This article describes the typical properties and functions of Estonian -mine action nominals, using dialect corpus data. The dialect data entails non-standard spoken language with a regional dimension and therefore has the potential to display more variation in terms of the behaviour of action nominals in actual language use. This will be demonstrated, inter alia, by the non-canonical realization of arguments, e.g. retaining the sentential form of the patient argument, in phrases headed by -mine action nominals. The article also discusses the problems of assigning a word class to the regularly derived and productive type of action nominals, when taking into account all the possible contexts and constructions in which they can occur.Kokkuvõte. Maarja-Liisa Pilvik: Deverbaalsed mine-teonimed eesti murrete korpuses. Artiklis kirjeldatakse eesti keele mine-teonimede tüüpilisi omadusi ja funktsioone, kasutades eesti murrete korpuse andmeid. Murdekorpus sisaldab mittestandardset kõneldud keelt, millel on ka geograafiline dimensioon, ning seetõttu on korpuse andmetel potentsiaal näidata mine-teonimede käitumises tegelikus keelekasutuses laiemat varieerumist. Seda ilmestab muuhulgas verbi argumentide mittekanooniline realiseerumine, nt patsienti väljendav lauseliige võib säilitada oma lauselise vormi nimisõnafraasides, mille peasõnaks mine-teonimi on. Artiklis puudutatakse ka probleeme, mis seonduvad regulaarselt tuletatavatele mine-teonimedele sõnaklassi määramisega, kui võtta arvesse kontekste ja konstruktsioone, milles mine-teonimed võivad esineda.Võtmesõnad: murdesüntaks; teonimed; nominalisatsioon; konstruktsioonid; eesti keel

Singular 2D Behaviors: Fornasini–Marchesini and Givone–Roesser Models

In this paper we study 2D Fornasini–Marchesini and 2D Givone–Roesser models from the viewpoint developed in our recent paper [Lomadze, Rogers, Wood, Georgian Math. J. 15: 139–157, 2008]. We give necessary and sufficient conditions for a behavior to be expressable in Fornasini–Marchesini or Givone–Roesser form, and a canonical realization when the conditions are met. We also study the regularity, controllability and autonomy of these models. In particular, we provide the concepts of controllability in the sense of Kalman for each model, and show that they agree with the behavioral controllability as defined in [Lomadze, Rogers, Wood, Georgian Math. J. 15: 139–157, 2008].

CANONICAL REALIZATIONS OF DOUBLY SPECIAL RELATIVITY

Doubly special relativity is usually formulated in momentum space, providing the explicit nonlinear action of the Lorentz transformations that incorporates the deformation of boosts. Various proposals have appeared in the literature for the associated realization in position space. While some are based on noncommutative geometries, others respect the compatibility of the space–time coordinates. Among the latter, there exist several proposals that invoke in different ways the completion of the Lorentz transformations into canonical ones in phase space. In this paper, the relationship between all these canonical proposals is clarified, showing that in fact they are equivalent. The generalized uncertainty principles emerging from these canonical realizations are also discussed in detail, studying the possibility of reaching regimes where the behavior of suitable position and momentum variables is classical, and explaining how one can reconstruct a canonical realization of doubly special relativity starting just from a basic set of commutators. In addition, the extension to general relativity is considered, investigating the kind of gravity's rainbow that arises from this canonical realization and comparing it with the gravity's rainbow formalism put forward by Magueijo and Smolin, which was obtained from a commutative but noncanonical realization in position space.