From 3D to 1D and Back to 2D

  • Guillaume LangEmail author
Part of the Springer Theses book series (Springer Theses)


We perceive the world as what mathematicians call a three-dimensional (3D) Euclidian space, providing a firm natural framework for geometry and physics until the modern times. Higher-dimensional real and abstract spaces have pervaded physics in the course of the twentieth century, through statistical physics where the number of degrees of freedom is comparable to the Avogadro number, quantum physics where huge Hilbert spaces are often involved, general relativity where in addition to a fourth spacetime dimension one considers curvature of a Riemannian manifold, or string theory where more dimensions are considered before compactification.


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  1. 1.Laboratoire de Physique et de Modélisation des Milieux Condensés (LPMMC)GrenobleFrance

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