Mathematical Physics

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» An Introduction to Noncommutative Geometry - A set of lecture notes by Joseph C. Varilly on noncommutative geometry and its applications in physics.
» Celestial Mechanics Research - Links, animations, references, and a brief description of research into n-body problems.
» Clyde Davenport's Commutative Hypercomplex Mathematics - Summary and application as it relates to electromagnetic theory and special relativity.
» 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.
» 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.
» Dimensional Analysis - A simple review of the powerful technique of dimensional analysis.
» Discrete Self-trapping Equation - A bibliography in BibTeX format for those interested in discrete nonlinear Schrödinger type equations.
» 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.
» Elastic Strain Soliton Visualization - Windows demonstration program download.
» 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.
» Five Lectures on Soliton Equations - A self-contained review by Edward Frenkel of a new approach to soliton equations of KdV type.
» Geometry and Duality - Lecture notes from the ITP miniprogram on Geometry and Duality
» 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.
» 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.
» Hyperreal World - Nonstandard analysis and its applications to quantum physics, by H.Yamashita. Mixed English/Japanese.
» Inexplicable Secrets of Creation - Relationships between number theory and physics.
» 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.
» Kinetic Theory and its Applications. - This resource is devoted to mathematical aspects of kinetic theory and its applications in physics and chemistry.
» Lectures on Orientifolds and Duality - Notes by Atish Dabholkar on orientifolds emphasizing applications to duality.
» 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).
» 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.
» Non Commutative Geometry - Preprints of Alejandro Rivero about Connes's NCG and the Standard Model. Also some historical articles on related topics.
» Open Problems in Mathematics and Physics - Links to open problems in mathematics, physics and other subjects.
» Period and energy in one degree of freedom systems - An article by Jorge Rezende, University of Lisbon (PDF).
» Radial Symmetric Fourier Transforms - Fourier transforms of radially-symmetric functions can be performed efficiently using the Hankel transform of order zero. Illustrations of the method are presented, and of the Gibbs' phenomenon.
» 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.
» Solitons - Resources at Heriot-Watt University. Meetings, local and other links.
» Symplectic Geometries in Quantum Physics and Optics - A comparison of symplectic geometry with Euclidean or unitary geometries in quantum physics and optics
» The Dirac Delta Function - A brief introduction to the properties and uses of the Dirac delta function.
» This Week's Finds in Mathematical Physics - This is a column written about modern topics in mathematical physics.
» Topology and Physics - An essay by C. Nash on the historical connection between topology and physics.
» Twistor Theory - Description of Twistor Theory
» Twistor Web - A new approach pioneered by Roger Penrose, starting with conformally-invariant concepts, to the synthesis of quantum theory and relativity. Some papers on-lin.
» Twistors- What are they? - A set of notes introducing spinors and twistors.
» Visual Mathematical Physics - Collection of animated gif pictures describing the solutions of the main partial differential equations such as Laplace, Poisson, string and membrane oscillations and heat conduction.