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Mathematical Physics
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Commutative Hypercomplex Mathematics - A commutative algebra, function theory, and system of analysis is developed for one 4-D variable (not quaternions). It is based upon a commutative group ring and extends all of the properties of the classical complex variables. |
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Complex Geometry of Nature and General Relativity - 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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Differential Equations and Oscillations - 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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Doing Physics with Quaternions - 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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Euclidean Geometric Transforms for Physics - 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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Holomorphic Methods in Mathematical Physics - 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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Homological Methods in Mathematical Physics - 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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Hyperreal World - Nonstandard analysis and its applications to quantum physics, by H.Yamashita. Mixed English/Japanese. |
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Intrinsic Localized Modes - Dynamics of defect-free periodic lattices in terms of plane wave phonons. Web text by Albert J. Sievers, Cornell. |
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Journal on Applied Clifford Algebra - 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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Klaus Brauer's Soliton Page - 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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Local Quantum Physics Crossroads - 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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Mathematical Methods I - 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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Non Commutative Geometry - Preprints of Alejandro Rivero about Connes's NCG and the Standard Model. Also some historical articles on related topics. |
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On the Origins of Twister Theory - A new approach pioneered by Roger Penrose, starting with conformally-invariant concepts, to the synthesis of quantum theory and relativity. |
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Recent Developments in Skyrme Models - 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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Solitons - An overview of the classical and quantum theory related to solitons |
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Solitons - Resources at Heriot-Watt University. Meetings, local and other links. |
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Topology and Physics - An essay by C. Nash on the historical connection between topology and physics. |
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