Mathematical Physics

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.
http://arxiv.org/abs/gr-qc/9911051

Open Problems in Mathematics and Physics - Links to open problems in mathematics, physics and other subjects.
http://www.geocities.com/ednitou/

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.
http://world.std.com/~sweetser/quaternions/qindex/qindex.html

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.
http://arxiv.org/abs/hep-th/9812148

Twistors- What are they? - A set of notes introducing spinors and twistors.
http://www.compsoc.net/~fedja/twistors/twistors.html

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.
http://clifford-algebras.org

This Week's Finds in Mathematical Physics - This is a column written about modern topics in mathematical physics.
http://math.ucr.edu/home/baez/TWF.html

Geometry and Duality - Lecture notes from the ITP miniprogram on Geometry and Duality
http://online.itp.ucsb.edu/online/geom/

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.
http://www.usf.uni-osnabrueck.de/~kbrauer/solitons.html

Solitons - An overview of the classical and quantum theory related to solitons
http://physics1.usc.edu/~vongehr/solitons_html/solitons.html

Topology and Physics - An essay by C. Nash on the historical connection between topology and physics.
http://arxiv.org/abs/hep-th/9709135

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.
http://w3.physics.uiuc.edu/~m-stone5/mma/mma.html

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.
http://www.physics.orst.edu/~rubin/nacphy/ComPhys/DIFFEQ/mydif2/

Hyperreal World - Nonstandard analysis and its applications to quantum physics, by H.Yamashita. Mixed English/Japanese.
http://www.sun-inet.or.jp/~leibniz/math/

Symplectic Geometries in Quantum Physics and Optics - A comparison of symplectic geometry with Euclidean or unitary geometries in quantum physics and optics
http://arxiv.org/abs/quant-ph/9509002

An Introduction to Noncommutative Geometry - A set of lecture notes by Joseph C. Varilly on noncommutative geometry and its applications in physics.
http://arxiv.org/abs/physics/9709045

Five Lectures on Soliton Equations - A self-contained review by Edward Frenkel of a new approach to soliton equations of KdV type.
http://arxiv.org/abs/q-alg/9712005

Dimensional Analysis - A simple review of the powerful technique of dimensional analysis.
http://www.physics.uoguelph.ca/tutorials/dimanaly/

Discrete Self-trapping Equation - A bibliography in BibTeX format for those interested in discrete nonlinear Schrödinger type equations.
http://www.ma.hw.ac.uk/~chris/dst/

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.
http://users.ox.ac.uk/~tweb/00001/

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.
http://arxiv.org/abs/quant-ph/9912054

Lectures on Orientifolds and Duality - Notes by Atish Dabholkar on orientifolds emphasizing applications to duality.
http://arxiv.org/abs/hep-th/9804208

Non Commutative Geometry - Preprints of Alejandro Rivero about Connes's NCG and the Standard Model. Also some historical articles on related topics.
http://dftuz.unizar.es/~rivero/research/index.html

Solitons - Resources at Heriot-Watt University. Meetings, local and other links.
http://www.ma.hw.ac.uk/solitons/

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.
http://arxiv.org/abs/math.DG/9808130

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).
http://www.lqp.uni-goettingen.de/lqp/

Period and energy in one degree of freedom systems - An article by Jorge Rezende, University of Lisbon. [PDF]
http://gfm.cii.fc.ul.pt/people/jrezende/jr_periodenergy1.pdf

Intrinsic Localized Modes - Dynamics of defect-free periodic lattices in terms of plane wave phonons. Web text by Albert J. Sievers, Cornell.
http://www.lassp.cornell.edu/~sievers/ilm/

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.
http://home.comcast.net/~cmdaven/hyprcplx.htm

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.
http://physicstransforms.tripod.com/

Inexplicable Secrets of Creation - Relationships between number theory and physics.
http://www.secamlocal.ex.ac.uk/~mwatkins/isoc/