Knowledge: mathematical physics
See Also:
Links
- Twistors- What are they?
http://www.compsoc.net/~fedja/twistors/twistors.html - A set of notes introducing spinors and twistors.
- Dimensional Analysis
http://www.physics.uoguelph.ca/tutorials/dimanaly/ - A simple review of the powerful technique of dimensional analysis.
- 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.
- Hyperreal World
http://www.sun-inet.or.jp/~leibniz/math/ - Nonstandard analysis and its applications to quantum physics, by H.Yamashita. Mixed English/Japanese.
- 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.
- This Week's Finds in Mathematical Physics
http://math.ucr.edu/home/baez/TWF.html - This is a column written about modern topics in mathematical physics.
- 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.
- Lectures on Orientifolds and Duality
http://arxiv.org/abs/hep-th/9804208 - Notes by Atish Dabholkar on orientifolds emphasizing applications to duality.
- 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.
- Recent Developments in Skyrme Models
http://arxiv.org/abs/hep-th/9812148 - 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 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.
- 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.
- Open Problems in Mathematics and Physics
http://www.geocities.com/ednitou/ - Links to open problems in mathematics, physics and other subjects.
- 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.
- Symplectic Geometries in Quantum Physics and Optics
http://arxiv.org/abs/quant-ph/9509002 - A comparison of symplectic geometry with Euclidean or unitary geometries in quantum physics and optics
- Topology and Physics
http://arxiv.org/abs/hep-th/9709135 - An essay by C. Nash on the historical connection between topology and physics.
- Period and energy in one degree of freedom systems
http://gfm.cii.fc.ul.pt/Members/jr_periodenergy1.pdf - An article by Jorge Rezende, University of Lisbon (PDF).
- 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.
- 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.
- 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).
- Solitons
http://physics1.usc.edu/~vongehr/solitons_html/solitons.html - An overview of the classical and quantum theory related to solitons
- The Dirac Delta Function
http://www.sci.hkbu.edu.hk/msc/full/billy/node5.html#SECTION00120000000000000000 - A brief introduction to the properties and uses of the Dirac delta function.
- Solitons
http://www.ma.hw.ac.uk/solitons/ - Resources at Heriot-Watt University. Meetings, local and other links.
- 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.
- Geometry and Duality
http://online.itp.ucsb.edu/online/geom/ - Lecture notes from the ITP miniprogram on Geometry and Duality
- 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.
- 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.
- 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.
- 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.
- On the Origins of Twister Theory
http://users.ox.ac.uk/~tweb/00001/ - A new approach pioneered by Roger Penrose, starting with conformally-invariant concepts, to the synthesis of quantum theory and relativity.
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