• Corpus ID: 119142393

Algebra of Noncommutative Riemann Surfaces

@article{Ohsaku2006AlgebraON,
  title={Algebra of Noncommutative Riemann Surfaces},
  author={Tadafumi Ohsaku},
  journal={arXiv: Mathematical Physics},
  year={2006}
}
  • Tadafumi Ohsaku
  • Published 21 June 2006
  • Mathematics
  • arXiv: Mathematical Physics
We examine several algebraic properties of the noncommutive $z$-plane and Riemann surfaces. The starting point of our investigation is a two-dimensional noncommutative field theory, and the framework of the theory will be converted into that of a complex coordinate system. The basis of noncommutative complex analysis is obtained thoroughly, and the considerations on functional analysis are also given before performing the examination of the conformal mapping and the Teichmuller theory… 
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4 Citations
Background Citations
2
Methods Citations
2

4 Citations

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References

SHOWING 1-10 OF 44 REFERENCES

Quantum field theory on noncommutative spaces

Topological Quantum Field Theory and Algebraic Structures

Summary. These notes are from lectures given at the Quantum field theory and noncommutative geometry workshop at Tohoku University in Sendai, Japan from November 24–30, 2002. We give a survey of…

A Short survey of noncommutative geometry

We give a survey of selected topics in noncommutative geometry, with some emphasis on those directly related to physics, including our recent work with Dirk Kreimer on renormalization and the…

String theory and noncommutative geometry

We extend earlier ideas about the appearance of noncommutative geometry in string theory with a nonzero B-field. We identify a limit in which the entire string dynamics is described by a minimally…

A Path Integral Approach¶to the Kontsevich Quantization Formula

Abstract: We give a quantum field theory interpretation of Kontsevich's deformation quantization formula for Poisson manifolds. We show that it is given by the perturbative expansion of the path…

Quantum Riemann surfaces I. The unit disc

AbstractWe construct a non-commutative ℂ*-algebra $$C_\mu (\bar U)$$ which is a quantum deformation of the algebra of continuous functions on the closed unit disc $$\bar U$$ . $$C_\mu (\bar U)$$ is…

Deformation Quantization of Poisson Manifolds

I prove that every finite-dimensional Poisson manifold X admits a canonical deformation quantization. Informally, it means that the set of equivalence classes of associative algebras close to the…

Supersymmetric Quantum Theory and Non-Commutative Geometry

Abstract:Classical differential geometry can be encoded in spectral data, such as Connes' spectral triples, involving supersymmetry algebras. In this paper, we formulate non-commutative geometry in…

Noncommutative field theory

We review the generalization of field theory to space-time with noncommuting coordinates, starting with the basics and covering most of the active directions of research. Such theories are now known…

Quantum fields and motives