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Statistical Mechanics
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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.
Topology and Physics
An essay by C. Nash on the historical connection between topology and physics.
Lectures on Orientifolds and Duality
Notes by Atish Dabholkar on orientifolds emphasizing applications to duality.
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.
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.
An Introduction to Noncommutative Geometry
A set of lecture notes by Joseph C. Varilly on noncommutative geometry and its applications in physics.
Five Lectures on Soliton Equations
A self-contained review by Edward Frenkel of a new approach to soliton equations of KdV type.
Symplectic Geometries in Quantum Physics and Optics
A comparison of symplectic geometry with Euclidean or unitary geometries in quantum physics and optics
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.
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.
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.
Non Commutative Geometry
Preprints of Alejandro Rivero about Connes's NCG and the Standard Model. Also some historical articles on related topics.
Period and energy in one degree of freedom systems
An article by Jorge Rezende, University of Lisbon (PDF).
Clyde Davenport's Commutative Hypercomplex Mathematics
Summary and application as it relates to electromagnetic theory and special relativity.
This Week's Finds in Mathematical Physics
This is a column written about modern topics in mathematical physics.
Geometry and Duality
Lecture notes from the ITP miniprogram on Geometry and Duality
Solitons
An overview of the classical and quantum theory related to solitons
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.
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.
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.
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.
Twistors- What are they?
A set of notes introducing spinors and twistors.
Open Problems in Mathematics and Physics
Links to open problems in mathematics, physics and other subjects.
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.
Intrinsic Localized Modes
Dynamics of defect-free periodic lattices in terms of plane wave phonons. Web text by Albert J. Sievers, Cornell.
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).
Solitons
Resources at Heriot-Watt University. Meetings, local and other links.
Discrete Self-trapping Equation
A bibliography in BibTeX format for those interested in discrete nonlinear Schrödinger type equations.
Celestial Mechanics Research
Links, animations, references, and a brief description of research into n-body problems.
Inexplicable Secrets of Creation
Relationships between number theory and physics.
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.
The Dirac Delta Function
A brief introduction to the properties and uses of the Dirac delta function.
Hyperreal World
Nonstandard analysis and its applications to quantum physics, by H.Yamashita. Mixed English/Japanese.
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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