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A set of lecture notes by Joseph C. Varilly on noncommutative geometry and its applications in physics.
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A paper by Giampiero Esposito attempting to give a self-contained introduction to holomorphic ideas in general relativity. The main topics are complex manifolds, spinor and twistor methods, heaven spaces.
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Many problems in physics are described by differential equations. As a complete discussion of differential equations is beyond the scope of this chapter we will deal only with linear first and second order ordinary differential equations.
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A simple review of the powerful technique of dimensional analysis.
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A bibliography in BibTeX format for those interested in discrete nonlinear Schrödinger type equations.
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A research effort to see how much of standard physics can be done using only quaternions, a 4-dimensional division algebra.
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A new method of correlating physics formulas to derive one formula from a related formula using Euclidean geometry to represent the inter-relationship of physics formulas.
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A self-contained review by Edward Frenkel of a new approach to soliton equations of KdV type.
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Lecture notes from the ITP miniprogram on Geometry and Duality
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This set of lecture notes by Brian C. Hall gives an introduction to holomorphic function spaces as used in mathematical physics. The emphasis is on the Segal-Bargmann space and the canonical commutation relations.
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These lecture notes by Joseph Krasil'shchik and Alexander Verbovetsky are a systematic and self-contained exposition of the cohomological theories naturally related to partial differential equations.
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Nonstandard analysis and its applications to quantum physics, by H.Yamashita. Mixed English/Japanese.
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Relationships between number theory and physics.
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Dynamics of defect-free periodic lattices in terms of plane wave phonons. Web text by Albert J. Sievers, Cornell.
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Journal devoted to the development of Geometric Analysis in particular through the use of Clifford Algebras, Quaternions, Hypercomplex Analysis and Multivector Techniques. Main emphasis en the applications to Physics.
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Presents a history of J.S.Russell's discovery of solitary waves, and animations of one-, two- and three-soliton solutions to the Korteweg-de Vries equation. Includes an article in PDF format on finding exact solutions to the KdV equation using the method of Backlund transform with the help of Mathematica.
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Notes by Atish Dabholkar on orientifolds emphasizing applications to duality.
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An international forum for information exchange among scientists working on mathematical, conceptual, and constructive problems in local relativistic quantum physics (LQP).
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This site contains the complete lecture notes and homework sets for PHYCS498MMA, a course of mathematical methods for physics given to entering graduate students, and senior undergraduates, at the University of Illinois at Urbana-Champaign.
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Preprints of Alejandro Rivero about Connes's NCG and the Standard Model. Also some historical articles on related topics.
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A new approach pioneered by Roger Penrose, starting with conformally-invariant concepts, to the synthesis of quantum theory and relativity.
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Links to open problems in mathematics, physics and other subjects.
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An article by Jorge Rezende, University of Lisbon (PDF).
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An introduction by T. Gisiger and M.B. Paranjape to recent, more mathematical developments in the Skyrme model. The aim is to render these advances accessible to mainstream nuclear and particle physicists.
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Resources at Heriot-Watt University. Meetings, local and other links.
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A comparison of symplectic geometry with Euclidean or unitary geometries in quantum physics and optics
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This is a column written about modern topics in mathematical physics.
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An essay by C. Nash on the historical connection between topology and physics.
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A set of notes introducing spinors and twistors.
