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Mathematical Physics
Directory > Science > Physics > Mathematical Physics
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  A new approach pioneered by Roger Penrose, starting with conformally-invariant concepts, to the synthesis of quantum theory and relativity. |
Resources at Heriot-Watt University. Meetings, local and other links. |
A bibliography in BibTeX format for those interested in discrete nonlinear Schrödinger type equations. |
Relationships between number theory and physics. |
Four seminars are held in rotation every year. |
A brief introduction to the properties and uses of the Dirac delta function. |
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. |
Dynamics of defect-free periodic lattices in terms of plane wave phonons. Web text by Albert J. Sievers, Cornell. |
An overview of the classical and quantum theory related to solitons |
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. |
How mathematics exists in the universe and is related to physical reality. |
A self-contained review by Edward Frenkel of a new approach to soliton equations of KdV type. |
An essay by C. Nash on the historical connection between topology and physics. |
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. |
Notes by Atish Dabholkar on orientifolds emphasizing applications to duality. |
A comparison of symplectic geometry with Euclidean or unitary geometries in quantum physics and optics |
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. |
A set of lecture notes by Joseph C. Varilly on noncommutative geometry and its applications in physics. |
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. |
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. |
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. |
This is a column written about modern topics in mathematical physics. |
Lecture notes from the ITP miniprogram on Geometry and Duality |
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. |
A set of notes introducing spinors and twistors. |
Journal devoted to the development of Geometric Analysis in particular through the use of Clifford Algebras, Quaternions, Hypercomplex Analysis and Multivector Techniques. Main emphasis on the applications to Physics. |
A simple review of the powerful technique of dimensional analysis. |
An international forum for information exchange among scientists working on mathematical, conceptual, and constructive problems in local relativistic quantum physics (LQP). |
An article by Jorge Rezende, University of Lisbon. |
Preprints of Alejandro Rivero about Connes's NCG and the Standard Model. Also some historical articles on related topics. |
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. |
Nonstandard analysis and its applications to quantum physics, by H.Yamashita. Mixed English/Japanese. |
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. |
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