Research ArticlesNo Access

SCALAR FIELD ON NON-INTEGER-DIMENSIONAL SPACES

R. TRINCHERO

Instituto Balseiro y Centro Atómico Bariloche, Argentina

https://doi.org/10.1142/S0219887812500703Cited by:7 (Source: Crossref)

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.

Keywords:

References

A. Connes , Noncommutative Geometry ( Academic Press , 1994 ) . Google Scholar
J. Madore , An Introduction to Noncommutative Differential Geometry and Its Applications ( Cambridge University Press , 2000 ) . Google Scholar
G. Landi , Introduction to Noncommutative Spaces and Their Geometries ( Springer-Verlag , New York , 1997 ) . Google Scholar
J. M. Gracia-Bondia , J. C. Varilly and H. Figueroa , Elements of Noncommutative Geometry ( Birkhäuser , Boston , 2000 ) . Google Scholar
A. Connes and H. Moscovici, Geom. Funct. Anal. 5, 174 (1995), DOI: 10.1007/BF01895667. Crossref, Web of Science, Google Scholar
E. Christensen, C. Ivan and M. L. Lapidus, Adv. Math. 217, 42 (2008), DOI: 10.1016/j.aim.2007.06.009. Crossref, Web of Science, Google Scholar
J. Collins , Renormalization ( Cambridge University Press , 1984 ) . Crossref, Google Scholar
R. Trinchero, Examples of non-integer-dimensional geometries, preprint (2008) , arXiv:0809.4678 . Google Scholar
M. Douglas and N. Nekrasov, Rev. Mod. Phys. 73, 977 (2001), DOI: 10.1103/RevModPhys.73.977. Crossref, Web of Science, Google Scholar