2007International Journal of Modern Physics AOpen access

INTERNAL SPACE FOR THE NONCOMMUTATIVE GEOMETRY STANDARD MODEL AND STRINGS

Fedele Lizzi

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Abstract

In this paper I discuss connections between the noncommutative geometry approach to the Standard Model on one side, and the internal space coming from strings on the other. The Standard Model in noncommutative geometry is described via the spectral action. I argue that an internal noncommutative manifold compactified at the renormalization scale, could give rise to the almost commutative geometry required by the spectral action. I then speculate how this could arise from the noncommutative geometry given by the vertex operators of a string theory.

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What this paper is about

In this paper I discuss connections between the noncommutative geometry approach to the Standard Model on one side, and the internal space coming from strings on the other. The Standard Model in noncommutative geometry is described via the spectral action. I argue that an internal noncommutative manifold compactified at the renormalization scale, could give rise to the almost commutative geometry required by the spectral action. I then speculate how this could arise from the noncommutative geometry given by the vertex operators of a string theory.

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Available abstract

In this paper I discuss connections between the noncommutative geometry approach to the Standard Model on one side, and the internal space coming from strings on the other. The Standard Model in noncommutative geometry is described via the spectral action. I argue that an internal noncommutative manifold compactified at the renormalization scale, could give rise to the almost commutative geometry required by the spectral action. I then speculate how this could arise from the noncommutative geometry given by the vertex operators of a string theory.

Key concepts: Noncommutative geometry, Physics, Noncommutative quantum field theory, Quantum differential calculus, Spectral triple, Noncommutative algebraic geometry, Commutative property, String theory

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