How to Reduce Practically Any Problem to One Dimension

  • Daniel C. Mattis
Conference paper
Part of the Springer Series in Solid-State Sciences book series (SSSOL, volume 23)

Abstract

A large number of interesting problems of theoretical physics are exactly soluble in one spatial dimension (1D). These include studies in statistical mechanics of interacting or of random systems (solved by diagonalization of a transfer matrix), many-body problems (solved by a Bethe ansatz), nonlinear dynamics (leading to solitons), magnetism (reducible by the Jordan-Wigner transformation to a many-fermion problem), etc. Some of these studies apply to physically interesting systems such as polymers, magnetic molecules, and energy transport in long chain molecules, yet others might appear to be of academic interest only. Surprisingly, even some far-fetched work in 1D may ultimately find important physical applications in three spatial dimensions. In this paper I shall endeavor to demonstrate what sorts of problems, arising in arbitrary dimensions, can be successfully reduced to 1D where they can be analyzed and ultimately solved.

Keywords

Soliton Stein Kelly Summing 

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Copyright information

© Springer-Verlag Berlin Heidelberg 1981

Authors and Affiliations

  • Daniel C. Mattis
    • 1
  1. 1.Physics DepartmentUniversity of UtahSalt Lake CityUSA

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