Directory of Mathematical Physics Resources

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Sites which focus application of advanced mathematical topics in physical systems.

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• Academic Departments
• Calculus of Variations
• Courses
• Differential Equations
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• Geometric Algebra
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• Statistical Mechanics
• Topological Quantum Field Theory

Resources in This Category

• (UK) North British Mathematical Physics Seminar

  http://www.maths.ed.ac.uk/NBMPS/
  Four seminars are held in rotation every year.

• 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.

• 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.

• 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.

• Dimensional Analysis

  http://www.physics.uoguelph.ca/tutorials/dimanaly/
  A simple review of the powerful technique of dimensional analysis.

• 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.

• 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.

• 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.

• Geometry and Duality

  http://online.itp.ucsb.edu/online/geom/
  Lecture notes from the ITP miniprogram on Geometry and Duality

• 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.

• 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.

• Inexplicable Secrets of Creation

  http://www.secamlocal.ex.ac.uk/~mwatkins/isoc/
  Relationships between number theory and physics.

• Lectures on Orientifolds and Duality

  http://arxiv.org/abs/hep-th/9804208
  Notes by Atish Dabholkar on orientifolds emphasizing applications to duality.

• 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).

• Mathematical Physics

  http://www1.uprh.edu/rbaretti/
  Numerical codes are provided for a variety of problems. From the University of Puerto Rico at Humacao.

• On Mathematics, Mathematical Physics, Truth and Reality

  http://www.spaceandmotion.com/mathematical-physics/logic-truth-reality.htm
  How mathematics exists in the universe and is related to physical reality.

• 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.

• Open Problems in Mathematics and Physics

  http://www.openproblems.net/
  Links to open problems in mathematics, physics and other subjects.

• Period and Energy in One Degree of Freedom Systems

  http://gfm.cii.fc.ul.pt/people/jrezende/jr_periodenergy1.pdf
  An article by Jorge Rezende, University of Lisbon.

• 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.

• Solitons

  http://www.ma.hw.ac.uk/solitons/
  Resources at Heriot-Watt University. Meetings, local and other links.

• 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

• 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.

• Topology and Physics

  http://arxiv.org/abs/hep-th/9709135
  An essay by C. Nash on the historical connection between topology and physics.

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