• Corpus ID: 14245199

The Structure of Spacetime and Noncommutative Geometry

  title={The Structure of Spacetime and Noncommutative Geometry},
  author={Fedele Lizzi},
  • 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 

Figures from this paper

Noncommutativity as a mapping of paths

A reinterpretation of noncommutativity as a mapping of paths is proposed at the level of quantum mechanics.

Noncommutative gauge theory using a covariant star product defined between Lie-valued differential forms

We develop an internal gauge theory using a covariant star product. The space-time is a symplectic manifold endowed only with torsion but no curvature. It is shown that, in order to assure the

A possibility on prohibition of Higgs mass by the extended Lorentz transformation in noncommutative geometry

In this letter, we propose the extended Lorentz transformation in noncommutative geometry, as a possibility on protection of the Higgs mass. In order to reconcile this transformation with the

Peculiarities of Transition to Chaos in Nonideal Hydrodynamics Systems

The nonideal deterministic dynamic system ”tank with a fluid–electromotor” is considered. On the basis of investigation of low-dimensional mathematical model of the given system the map of dynamic

Non-commutativity in polar coordinates

We reconsider the fundamental commutation relations for non-commutative $$\mathbb {R}^{2}$$R2 described in polar coordinates with non-commutativity parameter $$\theta $$θ. Previous analysis found


In this study the general theoretical framework of Complexity theory is presented, viewed through non-extensive statistical theory introduced by Constantino Tsallis in 1988. Nonlinear dynamics,

Understanding the Multi-Scale and Multi-fractal Dynamics of Space Plasmas Through Tsallis Non-Extensive Statistical Theory

In this study it is shown that the Tsallis q-extended statistical theory was found efficient to describe faithfully the space plasmas statistics in every case, from the planetic magnetospheres, to

Mind Before Matter: Reversing the Arrow of Fundamentality

In this contribution, I suggest that it is sometimes a step forward to reverse our intuition on “what is fundamental”, a move that is somewhat reminiscent of the idea of noncommutative geometry. I

Universality of Tsallis Non-Extensive Statistics and Fractal Dynamics for Complex Systems

Tsallis q-extension of statistics and fractal generalization of dynamics are two faces of the same physical reality, as well as the Kernel modern complexity theory. The fractal generalization



Remarks on inflation and noncommutative geometry

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

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

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

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

Quantum field theory on noncommutative spaces


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

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

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