Open Directory - Science: Physics: Mathematical Physics
See also: This category in other languages: - Four seminars are held in rotation every year. - A set of lecture notes by Joseph C. Varilly on noncommutative geometry and its applications in physics. - 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. - 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. - 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. - A simple review of the powerful technique of dimensional analysis. - A bibliography in BibTeX format for those interested in discrete nonlinear Schrödinger type equations. - A research effort to see how much of standard physics can be done using only quaternions, a 4-dimensional division algebra. - 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. - A self-contained review by Edward Frenkel of a new approach to soliton equations of KdV type. - Lecture notes from the ITP miniprogram on Geometry and Duality - 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. - 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. - 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. - 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. - Notes by Atish Dabholkar on orientifolds emphasizing applications to duality. - An international forum for information exchange among scientists working on mathematical, conceptual, and constructive problems in local relativistic quantum physics (LQP). - 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. - Numerical codes are provided for a variety of problems. From the University of Puerto Rico at Humacao. - Preprints of Alejandro Rivero about Connes's NCG and the Standard Model. Also some historical articles on related topics. - NDAPortal.com is a free online repository and community dealing with uncertainty and variability in applied mechanics and engineering that explains the application of probabilistic and possibilistic methods in engineering projects. - How mathematics exists in the universe and is related to physical reality. - A new approach pioneered by Roger Penrose, starting with conformally-invariant concepts, to the synthesis of quantum theory and relativity. - Links to open problems in mathematics, physics and other subjects. - An article by Jorge Rezende, University of Lisbon. [PDF] - 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. - An overview of the classical and quantum theory related to solitons - Resources at Heriot-Watt University. Meetings, local and other links. - A comparison of symplectic geometry with Euclidean or unitary geometries in quantum physics and optics - A brief introduction to the properties and uses of the Dirac delta function. [PDF] - This is a column written about modern topics in mathematical physics. - An essay by C. Nash on the historical connection between topology and physics.
