• Corpus ID: 42917683

On model theory , non-commutative geometry and physics

  title={On model theory , non-commutative geometry and physics},
  author={Boris Zilber},
1.1 Our motivation for working on the subject presented below comes from the realisation of the rather paradoxical situation with the mathematics used by physicists in the last 70 or so years. Physicists have always been ahead of mathematicians in introducing and testing new methods of calculations, leaving to mathematicians the task of putting the new methods and ideas on a solid and rigorous foundation. But this time, with developments in quantum field theory huge progress achieved by… 

On approximations of Feynman path integrals

In [HH1], a paper inspired by the work [Zi] of B. Zilber on model theory of quantum mechanics, we studied finite dimensional approximations of the standard (von Neumann, operator) model for quantum


We study covers of the multiplicative group of an algebraically closed field as quasi- minimal pregeometry structures and prove that they satisfy the axioms for Zariski-like structures presented in

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We start by showing how to approximate unitary and bounded self-adjoint operators by operators in finite dimensional spaces. Using ultraproducts we give a precise meaning for the approximation. In

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Model Theory with Applications to Algebra and Analysis: A class of quantum Zariski geometries

This paper is an attempt to understand the nature of non-classical Zariski geometries. Examples of such structures were first discovered in [HZ]. These examples showed that contrary to some

Gromov-Hausdorff Distance for Quantum Metric Spaces/Matrix Algebras Converge to the Sphere for Quantum Gromov-Hausdorff Distance

Gromov-Hausdorff distance for quantum metric spaces Bibliography Matrix algebras Converge to the sphere for quantum Gromov-Hausdorff distance Bibliography.

Two remarks on differential fields . In Model theory and applications

  • Quad . Mat .
  • 2002

On Space and Time, ed. S.Majid

  • 2008

Kowalski Analytic number theory American Mathematical Society