• Corpus ID: 14245199

# The Structure of Spacetime and Noncommutative Geometry

@inproceedings{Lizzi2008TheSO,
title={The Structure of Spacetime and Noncommutative Geometry},
author={Fedele Lizzi},
year={2008}
}
• F. Lizzi
• Published 3 November 2008
• Mathematics
We give a general and nontechnical review of some aspects of noncommutative geometry as a tool to understand the structure of spacetime. We discuss the motivations for the constructions of a noncommutative geometry, and the passage from commutative to non
11 Citations

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## References

SHOWING 1-10 OF 70 REFERENCES

### Remarks on inflation and noncommutative geometry

• Physics
• 2001
We briefly discuss some possible cosmological implications of noncommutative geometry. While the noncommutativity we consider does not affect gravity, it can play an important role in the dynamics of

### An Introduction to Noncommutative Spaces and Their Geometries

Noncommutative Spaces and Algebras of Functions.- Projective Systems of Noncommutative Lattices.- Modules as Bundles.- A Few Elements of K-Theory.- The Spectral Calculus.- Noncommutative Differential

### Noncommutative Symmetries and Gravity

Spacetime geometry is twisted (deformed) into noncommutative spacetime geometry, where functions and tensors are now star-multiplied. Consistently, spacetime diffeomorhisms are twisted into

### Noncommutative quantum field theory: a confrontation of symmetries

• Mathematics
• 2008
The concept of a noncommutative field is formulated based on the interplay between twisted Poincare symmetry and residual symmetry of the Lorentz group. Various general dynamical results supporting

### Twisted Noncommutative Field Theory with the Wick-Voros and Moyal Products

• Physics
• 2008
We present a comparison of the noncommutative field theories built using two different star products: Moyal and Wick-Voros (or normally ordered). For the latter we discuss both the classical and the

### Elements of Noncommutative Geometry

• Mathematics
• 2000
This volume covers a wide range of topics including sources of noncommutative geometry; fundamentals of noncommutative topology; K-theory and Morita equivalance; noncommutative integrodifferential

### GENERALIZED WEYL SYSTEMS AND κ-MINKOWSKI SPACE

• Mathematics
• 2002
We introduce the notion of generalized Weyl system, and use it to define *-products which generalize the commutation relations of Lie algebras. In particular we study in a comparative way various

### Target Space Duality in Noncommutative Geometry

• Mathematics
• 1997
The structure of spacetime duality and discrete world sheet symmetries of compactified string theory is examined within the framework of noncommutative geometry. The full noncommutative string

### String theory and noncommutative geometry

• Mathematics, Physics
• 1999
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