A set of notes introducing spinors and twistors.

A simple review of the powerful technique of dimensional analysis.

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.

Nonstandard analysis and its applications to quantum physics, by H.Yamashita. Mixed English/Japanese.

A bibliography in BibTeX format for those interested in discrete nonlinear Schrödinger type equations.

This is a column written about modern topics 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.

Notes by Atish Dabholkar on orientifolds emphasizing applications to duality.

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.

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.

A set of lecture notes by Joseph C. Varilly on noncommutative geometry and its applications in 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.

Links to open problems in mathematics, physics and other subjects.

Preprints of Alejandro Rivero about Connes's NCG and the Standard Model. Also some historical articles on related topics.

A comparison of symplectic geometry with Euclidean or unitary geometries in quantum physics and optics

An essay by C. Nash on the historical connection between topology and physics.

An article by Jorge Rezende, University of Lisbon (PDF).

A self-contained review by Edward Frenkel of a new approach to soliton equations of KdV type.

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.

An international forum for information exchange among scientists working on mathematical, conceptual, and constructive problems in local relativistic quantum physics (LQP).

An overview of the classical and quantum theory related to solitons

Resources at Heriot-Watt University. Meetings, local and other links.

A research effort to see how much of standard physics can be done using only quaternions, a 4-dimensional division algebra.

Lecture notes from the ITP miniprogram on Geometry and Duality

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.

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.

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.

Relationships between number theory and physics.

Dynamics of defect-free periodic lattices in terms of plane wave phonons. Web text by Albert J. Sievers, Cornell.

A new approach pioneered by Roger Penrose, starting with conformally-invariant concepts, to the synthesis of quantum theory and relativity.