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Calculus of Variations@ Differential Equations@
Geometric Algebra@ Statistical Mechanics
Topological Quantum Field Theory@  

See Also:

  • 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.
  • 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.
  • 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.
  • Solitons: An overview of the classical and quantum theory related to solitons
  • 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.

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