Canonical group quantization and boundary conditions

In the present thesis, we study quantization of classical systems with non-trivial phase spaces using the group-theoretical quantization technique proposed by Isham. Our main goal is a better understanding of global and topological aspects of quantum theory. In practice, the group-theoretical approach enables direct quantization of systems subject to constraints and boundary conditions in a natural and physically transparent manner -- cases for which the canonical quantization method of Dirac fails. First, we provide a clarification of the quantization formalism. In contrast to prior treatments, we introduce a sharp distinction between the two group structures that are involved and explain their physical meaning. The benefit is a consistent and conceptually much clearer construction of the Canonical Group. In particular, we shed light upon the 'pathological' case for which the Canonical Group must be defined via a central Lie algebra extension and emphasise the role of the central extension in general. In addition, we study direct quantization of a particle restricted to a half-line with 'hard wall' boundary condition. Despite the apparent simplicity of this example, we show that a naive quantization attempt based on the cotangent bundle over the half-line as classical phase space leads to an incomplete quantum theory; the reflection which is a characteristic aspect of the 'hard wall' is not reproduced. Instead, we propose a different phase space that realises the necessary boundary condition as a topological feature and demonstrate that quantization yields a suitable quantum theory for the half-line model. The insights gained in the present special case improve our understanding of the relation between classical and quantum theory and illustrate how contact interactions may be incorporated.

Fourier duality as a quantization principle

The Weyl-Wigner prescription for quantization on Euclidean phase spaces makes essential use of Fourier duality. The extension of this property to more general phase spaces requires the use of Kac algebras, which provide the necessary background for the implementation of Fourier duality on general locally compact groups. Kac algebras - and the duality they incorporate - are consequently examined as candidates for a general quantization framework extending the usual formalism. Using as a test case the simplest nontrivial phase space, the half-plane, it is shown how the structures present in the complete-plane case must be modified. Traces, for example, must be replaced by their noncommutative generalizations - weights - and the correspondence embodied in the Weyl-Wigner formalism is no longer complete. Provided the underlying algebraic structure is suitably adapted to each case, Fourier duality is shown to be indeed a very powerful guide to the quantization of general physical systems.

Remark on the vectorlike nature of electromagnetism and electric charge quantization

In this work we study the structure of electromagnetic interactions and electric charge quantization in gauge theories of electroweak interactions based on semisimple groups. We show that in the standard model of electroweak interactions the structure of electromagnetic interactions is strongly correlated to the quantization pattern of electric charges. We examine these two questions also in all possible chiral bilepton gauge models of electroweak interactions. In all, we can explain the vectorlike nature of electromagnetic interactions and electric charge quantization together demanding nonvanishing fermion masses and anomaly cancellations. ©1999 The American Physical Society.

Working in groups

This chapter is a condensation of a guide written by the chapter authors for both university teachers and students (Fowler et al., 2006). All page references given in this chapter are to this guide, unless otherwise stated. University students often work in groups. It may be a formal group (i.e. one that has been formed for a group presentation, writing a report, or completing a project) or an informal group (i.e. some students have decided to form a study group or undertake research together). Whether formal or informal, this chapter aims to make working in groups easier for you. Health care professionals also often work in groups. Yes, working in groups will extend well beyond your time at university. In fact, the skills and abilities to work effectively in groups are some of the most sought-after attributes in health care professionals. It seems obvious, then, that taking the opportunity to develop and enhance your skills and abilities for working in groups is a wise choice.

A comparison of the hazard perception ability of matched groups of healthy drivers aged 35 to 55, 65 to 74, and 75 to 84 years

We examined differences in response latencies obtained during a validated video-based hazard perception driving test between three healthy, community-dwelling groups: 22 mid-aged (35-55 years), 34 young-old (65-74 years), and 23 old-old (75-84 years) current drivers, matched for gender, education level, and vocabulary. We found no significant difference in performance between mid-aged and young-old groups, but the old-old group was significantly slower than the other two groups. The differences between the old-old group and the other groups combined were independently mediated by useful field of view (UFOV), contrast sensitivity, and simple reaction time measures. Given that hazard perception latency has been linked with increased crash risk, these results are consistent with the idea that increased crash risk in older adults could be a function of poorer hazard perception, though this decline does not appear to manifest until age 75+ in healthy drivers.

Demographic category membership and leadership in small groups : a social identity analysis

Developing the social identity theory of leadership (e.g., [Hogg, M. A. (2001). A social identity theory of leadership. Personality and Social Psychology Review, 5, 184–200]), an experiment (N=257) tested the hypothesis that as group members identify more strongly with their group (salience) their evaluations of leadership effectiveness become more strongly influenced by the extent to which their demographic stereotype-based impressions of their leader match the norm of the group (prototypicality). Participants, with more or less traditional gender attitudes (orientation), were members, under high or low group salience conditions (salience), of non-interactive laboratory groups that had “instrumental” or “expressive” group norms (norm), and a male or female leader (leader gender). As predicted, these four variables interacted significantly to affect perceptions of leadership effectiveness. Reconfiguration of the eight conditions formed by orientation, norm and leader gender produced a single prototypicality variable. Irrespective of participant gender, prototypical leaders were considered more effective in high then low salience groups, and in high salience groups prototypical leaders were more effective than less prototypical leaders. Alternative explanations based on status characteristics and role incongruity theory do not account well for the findings. Implications of these results for the glass ceiling effect and for a wider social identity analysis of the impact of demographic group membership on leadership in small groups are discussed.