Derivation of the total twist from Chern-Simons theory

The total twist number, which represents the first non-trivial Vassiliev knot invariant, is derived from the second order expression of the Wilson loop expectation value in the Chern-Simons theory. Using the well-known fact that the analytical expression is an invariant, a non-recursive formulation of the total twist based on the evaluation of knot diagrams is constructed by an appropriate deformation of the knot line in the three-dimensional Euclidian space. The relation to the original definition of the total twist is elucidated.Comment: 26 page

Seeing Earth's Orbit in the Stars: Parallax and Aberration

During the 17th century the idea of an orbiting and rotating Earth became increasingly popular, but opponents of this view continued to point out that the theory had observable consequences that had never, in fact, been observed. Why, for instance, had astronomers failed to detect the annual parallax of the stars that must occur if Earth orbits the Sun? To address this problem, astronomers of the 17th and18th centuries sought to measure the annual parallax of stars using telescopes. None of them succeeded. Annual stellar parallax was not successfully measured until 1838, when Friedrich Bessel detected the parallax of the star 61 Cygni. But the early failures to detect annual stellar parallax led to the discovery of a new (and entirely unexpected) phenomenon: the aberration of starlight. This paper recounts the story of the discovery of stellar aberration. It is accompanied by a set of activities and computer simulations that allow students to explore this fascinating historical episode and learn important lessons about the nature of science.Comment: 10 pages, 5 figures, submitted to The Physics Teache

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 canonical quantization procedure for systems with either bosonic of fermionic degrees of freedom. We illustrate this procedure for a number a 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.Comment: 21 page

Leduc-Righi effect in superconductors with nontrivial density of states

Increasing of electronic thermal conductivity of superconductor in the model with nontrivial density of states was considered. The electronic thermal conductivity K(T) of SC in the presence of external magnetic field was investigated. It was shown that if symmetrical part of quasiparticle scattering rate less than cyclotron energy observed mechanism of increasing K(T) can be separated from connected with asymmetric electronic scattering effects another one.Comment: 5 pages, RevTe

Sources Of Student Engagement In Introductory Physics For Life Sciences

We explore the sources of student engagement with curricular content in an Introductory Physics for Life Science (IPLS) course at Swarthmore College. Do IPLS students find some life-science contexts more interesting than others, and, if so, what are the sources of these differences? We draw on three sources of student data to answer this question: (1) quantitative survey data illustrating how interested students were in particular contexts from the curriculum, (2) qualitative survey data in which students describe the source of their interest in these particular contexts, and (3) interview data in which students reflect on the contexts that were and were not of interest to them. We find that examples that make interdisciplinary connections with students’ other coursework in biology and chemistry, and examples that make connections to what students perceive to be the “real world,” are particularly effective at fostering interest. More generally, students describe being deeply engaged with contexts that foster a sense of coherence or have personal meaning to them. We identify various “engagement pathways” by which different life-science students engage with IPLS content, and suggest that a curriculum needs to be flexible enough to facilitate these different pathways

Star Products and Geometric Algebra

The formalism of geometric algebra can be described as deformed super analysis. The deformation is done with a fermionic star product, that arises from deformation quantization of pseudoclassical mechanics. If one then extends the deformation to the bosonic coefficient part of superanalysis one obtains quantum mechanics for systems with spin. This approach clarifies on the one hand the relation between Grassmann and Clifford structures in geometric algebra and on the other hand the relation between classical mechanics and quantum mechanics. Moreover it gives a formalism that allows to handle classical and quantum mechanics in a consistent manner.Comment: 21 page

Deformation Quantization of Fermi Fields

Deformation quantization for any Grassmann scalar free field is described via the Weyl-Wigner-Moyal formalism. The Stratonovich-Weyl quantizer, the Moyal $\star$-product and the Wigner functional are obtained by extending the formalism proposed recently in [35] to the fermionic systems of infinite number of degrees of freedom. In particular, this formalism is applied to quantize the Dirac free field. It is observed that the use of suitable oscillator variables facilitates considerably the procedure. The Stratonovich-Weyl quantizer, the Moyal $\star$-product, the Wigner functional, the normal ordering operator, and finally, the Dirac propagator have been found with the use of these variables.Comment: 19+1 pages, no figures, revtex4 file styl

Introductory Physics In Biological Context: An Approach To Improve Introductory Physics For Life Science Students

We describe restructuring the introductory physics for life science students (IPLS) course to better support these students in using physics to understand their chosen fields. Our courses teach physics using biologically rich contexts. Specifically, we use examples in which fundamental physics contributes significantly to understanding a biological system to make explicit the value of physics to the life sciences. This requires selecting the course content to reflect the topics most relevant to biology while maintaining the fundamental disciplinary structure of physics. In addition to stressing the importance of the fundamental principles of physics, an important goal is developing students\u27 quantitative and problem solving skills. Our guiding pedagogical framework is the cognitive apprenticeship model, in which learning occurs most effectively when students can articulate why what they are learning matters to them. In this article, we describe our courses, summarize initial assessment data, and identify needs for future research. (C) 2014 American Association of Physics Teachers