Localizability in de Sitter space

An analogue of the Newton-Wigner position operator is defined for a massive neutral scalar field in de Sitter space. The one-particle subspace of the theory, consisting of positive-energy solutions of the Klein-Gordon equation selected by the Hadamard condition, is identified with an irreducible representation of de Sitter group. Postulates of localizability analogous to those written by Wightman for fields in Minkowski space are formulated on it, and a unique solution is shown to exist. A simple expression for the time-evolution of the operator is presented.Comment: Presentation improved; references adde

The Two-Point Function and the Effective Magnetic Field in Diluted Ising Models on the Cayley Tree

Some results on the two-point function and on the analytic structure of the momenta of the effective fugacity at the origin for a class of diluted ferromagnetic Ising models on the Cayley tree are presented.Comment: 22 page

Aspects of Two-Level Systems under External Time Dependent Fields

The dynamics of two-level systems in time-dependent backgrounds is under consideration. We present some new exact solutions in special backgrounds decaying in time. On the other hand, following ideas of Feynman, Vernon and Hellwarth, we discuss in detail the possibility to reduce the quantum dynamics to a classical Hamiltonian system. This, in particular, opens the possibility to directly apply powerful methods of classical mechanics (e.g. KAM methods) to study the quantum system. Following such an approach, we draw conclusions of relevance for ``quantum chaos'' when the external background is periodic or quasi-periodic in time.Comment: To appear in J. Phys. A. Mathematical and Genera

Multiple classical limits in relativistic and nonrelativistic quantum mechanics

The existence of a classical limit describing interacting particles in a second-quantized theory of identical particles with bosonic symmetry is proved. This limit exists in addition to a previously established classical limit with a classical field behavior, showing that the limit $\hbar \to 0$ of the theory is not unique. An analogous result is valid for a free massive scalar field: two distinct classical limits are proved to exist, describing a system of particles or a classical field. The introduction of local operators in order to represent kinematical properties of interest is shown to break the permutation symmetry under some localizability conditions, allowing the study of individual particle properties.Comment: 13 page

Activity settings in toddler classrooms and quality of group and individual interactions

This study examined the variation of interaction quality both at the group and child levels across different activity settings in toddler classrooms. Participants were 104 children, with an average of 30.4 months old, of which 53.8% were boys. Educator-child interactions, at the group level, and child interactions with their educators, peers and tasks, at the child level, were observed through video-recordings across four activity settings, namely free play, early academic activities, aesthetics/arts activities and meals. Group level interactions were observed with the CLASS Toddler, and child level interactions with the inCLASS Toddler. Results showed that the quality of interactions at the group and child levels varied across different activity settings, but not always in the same direction. Findings suggest that activity settings play an important role in explaining the quality of interactions experienced by toddlers. Implications for early childhood educators are discussed.info:eu-repo/semantics/acceptedVersio

Existence of the Bogoliubov S(g) operator for the (:ϕ4:)2(:\phi^4:)_2 quantum field theory

We prove the existence of the Bogoliubov S(g) operator for the $(:\phi^4:)_2$ quantum field theory for coupling functions $g$ of compact support in space and time. The construction is nonperturbative and relies on a theorem of Kisy\'nski. It implies almost automatically the properties of unitarity and causality for disjoint supports in the time variable.Comment: LaTeX, 24 pages, minor modifications, typos correcte