1998/03/17 by David J. Raymond, Raymond, David J.
Engineering · Physics and Astronomy · Social Sciences · #Experimental Learning in Engineering #Experimental and Theoretical Physics Studies #FOS: Physical sciences #Physics Education (physics.ed-ph) #Science Education and Pedagogy #physics.ed-ph
paper · pdf · doi:10.48550/arxiv.physics/9803023
12 pages, 7 figures, LaTeX
arxiv created 1998/03/17 · openalex publication_date 1998/03/17 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
If potential energy is the timelike component of a four-vector, then there must be a corresponding spacelike part which would logically be called the potential momentum. The potential four-momentum consisting of the potential momentum and the potential energy taken together is just the gauge field of the associated force times the charge associated with that force. The canonical momentum is the sum of the ordinary and potential momenta. Refraction of matter waves by a discontinuity in a gauge field can be used to explore the effects of gauge fields at an elementary level. Using this tool it is possible to show how the Lorentz force law of electromagnetism follows from gauge theory. The resulting arguments are accessible to students at the level of the introductory calculus-based physics course and tie together classical and quantum mechanics, relativity, gauge theory, and electromagnetism. The resulting economy of presentation makes it easier to include modern physics in the one year course normally available for teaching introductory physics.