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arXiv · 1201.4365

Scalar field on non-integer dimensional spaces

R. Trinchero
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Abstract

Deformations of the canonical spectral triples over the n-dimensional torus are considered. These deformations have a discrete dimension spectrum consisting of non-integer values less than n. The differential algebra corresponding to these spectral triples is studied. No junk forms appear for non-vanishing deformation parameter. The action of a scalar field in these spaces is considered, leading to non-trivial extra structure compared to the integer dimensional cases, which does not involve a loss of covariance. One-loop contributions are computed leading to finite results for non-vanishing deformation.

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R. Trinchero. 2012-01-20. Scalar field on non-integer dimensional spaces. https://arxiv.org/abs/1201.4365

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