Gauge P-representations for quantum-dynamical problems: Removal of boundary terms

P-representation techniques, which have been very successful in quantum optics and in other fields, are also useful for general bosonic quantum-dynamical many-body calculations such as Bose-Einstein condensation. We introduce a representation called the gauge P representation, which greatly widens the range of tractable problems. Our treatment results in an infinite set of possible time evolution equations, depending on arbitrary gauge functions that can be optimized for a given quantum system. In some cases, previous methods can give erroneous results, due to the usual assumption of vanishing boundary conditions being invalid for those particular systems. Solutions are given to this boundary-term problem for all the cases where it is known to occur: two-photon absorption and the single-mode laser. We also provide some brief guidelines on how to apply the stochastic gauge method to other systems in general, quantify the freedom of choice in the resulting equations, and make a comparison to related recent developments.

Quantum symmetries and the Weyl–Wigner product of group representations

In the usual formulation of quantum mechanics, groups of automorphisms of quantum states have ray representations by unitary and antiunitary operators on complex Hilbert space, in accordance with Wigner's theorem. In the phase-space formulation, they have real, true unitary representations in the space of square-integrable functions on phase space. Each such phase-space representation is a Weyl–Wigner product of the corresponding Hilbert space representation with its contragredient, and these can be recovered by 'factorizing' the Weyl–Wigner product. However, not every real, unitary representation on phase space corresponds to a group of automorphisms, so not every such representation is in the form of a Weyl–Wigner product and can be factorized. The conditions under which this is possible are examined. Examples are presented.

A unified and complete construction of all finite dimensional irreducible representations of gl(2|2)

Representations of the non-semisimple superalgebra gl(2/2) in the standard basis are investigated by means of the vector coherent state method and boson-fermion realization. All finite-dimensional irreducible typical and atypical representations and lowest weight (indecomposable) Kac modules of gl(2/2) are constructed explicity through the explicit construction of all gl(2) circle plus gl(2) particle states (multiplets) in terms of boson and fermion creation operators in the super-Fock space. This gives a unified and complete treatment of finite-dimensional representations of gl(2/2) in explicit form, essential for the construction of primary fields of the corresponding current superalgebra at arbitrary level.

Useful representations of series solutions for transport problems

Simple techniques are presented for rearrangement of an infinite series in a systematic way such that the convergence of the resulting expression is accelerated. These procedures also allow calculation of required boundary derivatives. Several examples of conduction and diffusion-reaction problems illustrate the methods.

Children's understanding of pictorial and mental representations

Two studies demonstrate dissociation between children's understanding of pictorial representations (photos and drawings) and mental representations (beliefs). In Study 1, 37 preschoolers were tested on false belief, appearance-reality, false photo, and false drawing tasks. The false picture tasks were significantly easier, and no correlation was found between children's performances on false belief and false picture tasks. Ln Study 2, 30 children who failed a false belief pretest were randomly assigned to 3 training groups: Belief (trained on false belief tasks), Picture (trained on false picture tasks), or Control (trained on number conservation tasks). Training was conducted in 2 sessions over the course of 2 weeks, tasks were presented and feedback was provided. All children were posttested on theory of mind tasks, false picture tasks, and a number conservation task. The posttest results showed differential patterns of performance, with the Belief group scoring highest on the theory of mind posttests, the Picture group scoring highest on the false picture posttests, and the Control group scoring highest on the number conservation posttest. Results are discussed with respect to competing models of theory of mind development.

Attachment style, assertive communication, and safer-sex behavior

This research tested the proposition that the effect of attachment security on safer-sex practice may be mediated by communication patterns. One hundred eighty-five undergraduate students completed questionnaire measures of attachment, assertiveness, and attitudes to communication about AIDS. Eight weeks later, they reported on their practice of safer sex in the period since the first testing session. Hierarchical regressions showed that at Step 1, anxiety about relationships (a measure of insecure attachment) was associated with less safer-sex practice, for all outcome measures. Attitudes to communication about AIDS added to the prediction of general reports of safer-sex practice: in line with the mediational model, anxiety about relationships became unimportant as a predictor when communication variables were included. Communication variables failed to add to the prediction of safer sex on the most recent encounter, and both anxiety about relationships and attitudes to communication about AIDS predicted condom use. Some gender differences in patterns of prediction were noted. The results are discussed in terms of attachment style and its links with the negotiation of sexual practice and relationship issues.

Attachment style as a predictor of sexual attitudes and behavior in late adolescence

This research applied attachment theory to the study of sexual attitudes and behaviors in a sample of late adolescents. Four hundred and seventy heterosexual undergraduate students completed questionnaires assessing attachment (discomfort with closeness; anxiety over relationships), relationship history, communication about sex, sexual self-efficacy and locus of control, and attitudes to condoms. Eight weeks later, participants reported on sexual behaviors occurring during the eight-week interval, and perceived risk of these activities. Both discomfort with closeness and anxiety over relationships were associated with external locus of control for sexual outcomes, and with use of drugs before sexual contact. Anxiety over relationships was linked to unsafe sex and to negative attitudes to condoms, but discomfort with closeness was associated with a more cautious approach to sexual risk-taking. Some results were qualified by gender differences, and by differences between the full sample and those who were sexually active. The findings are discussed in terms of attachment style and its links with communication and affect regulation.

Level-one highest weight representations of U-q[g1(1 vertical bar 1)] and associated vertex operators

We study the level-one irreducible highest weight representations of U-q[gl(1\1)] and associated q-vertex operators. We obtain the exchange relations satisfied by these vertex operators. The characters and supercharacters associated with these irreducible representations are calculated'. (C) 2000 Published by Elsevier Science B.V. All rights reserved.