Physics: Mathematical Physics

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

Celestial Mechanics Research
http://www.math.washington.edu/~hampton/research.html
Links, animations, references, and a brief description of research into n-body problems.

Clyde Davenport's Commutative Hypercomplex Mathematics
http://home.usit.net/~cmdaven/cmdaven1.htm
Summary and application as it relates to electromagnetic theory and special relativity.

Complex Geometry of Nature and General Relativity
http://arxiv.org/abs/gr-qc/9911051
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
http://www.physics.orst.edu/~rubin/nacphy/ComPhys/DIFFEQ/mydif2/
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
http://www.physics.uoguelph.ca/tutorials/dimanaly/
A simple review of the powerful technique of dimensional analysis.

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

Doing Physics with Quaternions
http://world.std.com/~sweetser/quaternions/qindex/qindex.html
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
http://www.csa.ru/Inst/bogd_dep/nonlin/vizual.htm
Windows demonstration program download.

Euclidean Geometric Transforms for Physics
http://physicstransforms.tripod.com/
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
http://arxiv.org/abs/q-alg/9712005
A self-contained review by Edward Frenkel of a new approach to soliton equations of KdV type.

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

Holomorphic Methods in Mathematical Physics
http://arxiv.org/abs/quant-ph/9912054
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
http://arxiv.org/abs/math.DG/9808130
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
http://www.sun-inet.or.jp/~leibniz/math/
Nonstandard analysis and its applications to quantum physics, by H.Yamashita. Mixed English/Japanese.

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

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

Journal on Applied Clifford Algebra
http://clifford-algebras.org
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.
http://kinetic.boom.ru
This resource is devoted to mathematical aspects of kinetic theory and its applications in physics and chemistry.

Klaus Brauer's Soliton Page
http://www.usf.uni-osnabrueck.de/~kbrauer/solitons.html
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.

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

Local Quantum Physics Crossroads
http://www.lqp.uni-goettingen.de/lqp/
An international forum for information exchange among scientists working on mathematical, conceptual, and constructive problems in local relativistic quantum physics (LQP).

Mathematical Methods I
http://w3.physics.uiuc.edu/~m-stone5/mma/mma.html
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
http://dftuz.unizar.es/~rivero/research/index.html
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
http://www.geocities.com/ednitou
Links to open problems in mathematics, physics and other subjects.

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