arXiv subjects

Steuard Jensen

Publications and source records attributed to Steuard Jensen.

6 recordsLinked to original sources

arXiv2026

Teaching Maxwell's Equations from 2D to 3D with Bivectors

Electromagnetism is one of the few core physics topics without simple two-dimensional examples to start from: the cross product and curl require three dimensions. Previous work described magnetism as a bivector field, visualized with oriented (clockwise/counterclockwise) "tiles" rather than the traditional (pseudo)vector "arrows." Here, we express Maxwell's equations in this bivector language: magnetic flux is understood as a sum along a surface rather than through it, and the magnetic field tiles encircle the boundary of an Amperian loop or ribbon in a natural way. This allows a gentle two-dimensional starting point and makes symmetry arguments natural for magnetism.

physics.ed-ph↗

arXiv2024

Teaching Magnetism with Bivectors

The magnetic field is traditionally presented as a (pseudo)vector quantity, tied closely to the cross product. Though familiar to experts, many students find these ideas challenging and full of subtleties. Building on earlier work in rotational physics, we present an alternative pedagogical approach that describes magnetic fields using bivectors. These objects can be visualized as oriented tiles whose components form an antisymmetric matrix. Historically, bivectors have been mostly used in specialized contexts like spacetime classification or geometric algebra, but they are not necessarily more complicated to understand than cross products. Teaching magnetism in this language addresses common student difficulties, generalizes directly to relativity (and extra dimensions), and brings fresh insight to familiar ideas.

physics.ed-ph↗

arXiv2023

Teaching Rotational Physics with Bivectors

Angular momentum is traditionally taught as a (pseudo)vector quantity, tied closely to the cross product. This approach is familiar to experts but challenging for students, and full of subtleties. Here, we present an alternative pedagogical approach: angular momentum is described using bivectors, which can be visualized as "tiles" with area and orientation and whose components form an antisymmetric matrix. Although bivectors have historically been studied in specialized contexts like spacetime classification or geometric algebra, they are no more complicated to understand than cross products. The bivector language provides a more fundamental definition for rotational physics, and opens the door to understanding rotations in relativity and in extra dimensions.

physics.ed-ph↗

arXiv2023

Exploring entropy by counting microstates of the p-state paramagnet

Moore and Schroeder proposed an effective approach to introducing entropy and the second law through computational study of models with easily countable states at fixed energy. But such systems are rare: the only familiar examples are the Einstein solid and the two-state paramagnet, which limits the available questions for assignment or discussion. This work considers the more general p-state paramagnet and describes the modestly more complicated counting of its microstates. An instructor can draw on this family of systems to assign a variety of new problems or open-ended projects that students can complete with the help of a spreadsheet program or analytic calculation.

physics.ed-ph↗

arXiv2011

The KK-Monopole/NS5-Brane in Doubled Geometry

The Kaluza-Klein monopole has been recognized as a string background with significant non-geometric features: it must appear "localized" to winding strings to match the NS5-brane's localization on the T-dual circle. In this work, we explicitly construct this T-dual system in the doubled geometry formalism, which proves to successfully describe the duality despite a broken isometry on one side of the duality pair. We further suggest an extension of the doubled formalism to the gauged linear sigma models describing this system (both bosonic and supersymmetric) and show that previous calculations of worldsheet instanton effects are best understood in this doubled form.

hep-th↗

arXiv2005

Worldsheet Instanton Corrections to the Kaluza-Klein Monopole

The Kaluza-Klein monopole is a well known object in both gravity and string theory, related by T-duality to a "smeared" NS5-brane which retains the isometry around the duality circle. As the true NS5-brane solution is localized at a point on the circle, duality implies that the Kaluza-Klein monopole should show some corresponding behavior. In this paper, we express the Kaluza-Klein monopole as a gauged linear sigma model in two dimensions and show that worldsheet instantons give corrections to its geometry. These corrections can be understood as a localization in "winding space" which could be probed by strings with winding charge around the circle.

hep-th↗