Cliffordization, spin, and fermionic star products

Deformation quantization is a powerful tool for quantizing theories with bosonic and fermionic degrees of freedom. The star products involved generate the mathematical structures which have recently been used in attempts to analyze the algebraic properties of quantum field theory. In the context of quantum mechanics they provide a quantization procedure for systems with either bosonic or fermionic degrees of freedom. We illustrate this procedure for a number of physical examples, including bosonic, fermionic, and supersymmetric oscillators. We show how non-relativistic and relativistic particles with spin can be naturally described in this framework.     

Conceptions of function translation: obstacles, intuitions, and rerouting

A horizontal translation of a function is the focus of this study. We examine the explanations provided by secondary school students and secondary school teachers to a translation of a function, focusing on the example of the parabola y=(x−3)² and its relationship to y=x². The participants’ explanations focused on attending to patterns, locating the zero of the function, and the point-wise calculation of function values. The results confirm that the horizontal shift of the parabola is, at least initially, inconsistent with expectations and counterintuitive to most participants. We articulate possible sources of this perceived inconsistency and describe a pedagogical approach aimed at resolving it.     

Standardization of Methods for Characterizing the Surface Geometry of Solids

Since a comprehensive survey published in 1999 [1] much work was done in standardizing measuring methods to characterize the surface geometry of dispersed and/or porous solids and to certify reference materials. The present paper is an extension of a short communication [2]. It gives a survey on existing standards and reports on new drafts and proposals.     

Letter: Causality Violating Geodesics in Bonnor's Rotating Dust Metric

We exhibit timelike geodesic paths for a metric, introduced by Bonnor [11] and considered also by Steadman [13], and show that coordinate time runs backward along a portion of these geodesics.     

Space-Time Topology (II)—Causality, the Fourth Stiefel–Whitney Class and Space-Time as a Boundary

We show that stable causality is related to the vanishing of the top Stiefel–Whitney class of a space-time manifold M, and that if M is a stably causal space-time manifold, then it is the boundary of a five-dimensional space-time. We then propose a scheme for making it both a necessary and sufficient condition.     

What is a design? How should we classify them?

Design theory crosses the boundary between mathematics and statistics, and includes a wide range of disparate types of design. In this paper we present a classification scheme which aims to include as many important types as possible, based on a balance among concept, representation and use.