Demystifying the Lagrangians of special relativity

[2108.07786] Demystifying the Lagrangians of special relativity Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Physics > Classical Physics arXiv:2108.07786 (physics) [Submitted on 4 Jul 2021 ( v1 ), last revised 18 Aug 2021 (this version, v2)] Title: Demystifying the Lagrangians of special relativity Authors: Gerd Wagner , Matthew W. Guthrie View a PDF of the paper titled Demystifying the Lagrangians of special relativity, by Gerd Wagner and Matthew W. Guthrie View PDF HTML (experimental) Abstract: Special relativity beyond its basic treatment can be inaccessible, in particular because introductory physics courses typically view special relativity as decontextualized from the rest of physics. We seek to place special relativity back in its physics context, and to make the subject approachable. The Lagrangian formulation of special relativity follows logically by combining the Lagrangian approach to mechanics and the postulates of special relativity. In this paper, we derive and explicate some of the most important results of how the Lagrangian formalism and Lagrangians themselves behave in the context of special relativity. We derive two foundations of special relativity: the invariance of any spacetime interval, and the Lorentz transformation. We then develop the Lagrangian formulation of relativistic particle dynamics, including the transformation law of the electromagnetic potentials, the Lagrangian of a relativistic free particle, and Einstein's mass-energy equivalence law ($E=mc^2$). We include a discussion of relativistic field Lagrangians and their transformation properties, showing that the Lagrangians and the equations of motion for the electric and magnetic fields are indeed invariant under Lorentz transformations. Comments: Replaced to include an expanded introduction section Subjects: Classical Physics (physics.class-ph) Cite as: arXiv:2108.07786 [physics.class-ph] (or arXiv:2108.07786v2 [physics.class-ph] for this version) https://doi.org/10.48550/arXiv.2108.07786 Focus to learn more arXiv-issued DOI via DataCite Journal reference: Demystifying Classical Particles, Fields, and Relativity Through the Lagrangian Formalism. World Scientific, May 2026 Related DOI : https://doi.org/10.1142/14762 Focus to learn more DOI(s) linking to related resources Submission history From: Matthew Guthrie PhD [ view email ] [v1] Sun, 4 Jul 2021 18:07:15 UTC (34 KB) [v2] Wed, 18 Aug 2021 01:28:14 UTC (38 KB) Full-text links: Access Paper: View a PDF of the paper titled Demystifying the Lagrangians of special relativity, by Gerd Wagner and Matthew W. Guthrie View PDF HTML (experimental) TeX Source view license Current browse context: physics.class-ph < prev | next > new | recent | 2021-08 Change to browse by: physics References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

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