Scalar field on non-integer dimensional spaces

Details Scalar field on non-integer dimensional spaces Scalar field on non-integer dimensional spaces

2012-01-20

arxiv.org/abs/1201.4365v1

Physics

Mathematical Physics

16 pages, 2 figures

Scientific paper

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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