Fractal Theory Space: Spacetime of Noninteger Dimensionality

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dc.creatorHill, Christopher T.
dc.date2002-10-08
dc.date2002-10-29
dc.date.accessioned2026-07-07T11:48:03Z
dc.date.available2026-07-07T11:48:03Z
dc.descriptionWe construct matter field theories in ``theory space'' that are fractal, and invariant under geometrical renormalization group (RG) transformations. We treat in detail complex scalars, and discuss issues related to fermions, chirality, and Yang-Mills gauge fields. In the continuum limit these models describe physics in a noninteger spatial dimension which appears above a RG invariant ``compactification scale,'' M. The energy distribution of KK modes above M is controlled by an exponent in a scaling relation of the vacuum energy (Coleman-Weinberg potential), and corresponds to the dimensionality. For truncated-s-simplex lattices with coordination number s the spacetime dimensionality is 1+(3+2ln(s)/ln(s+2)). The computations in theory space involve subtleties, owing to the 1+3 kinetic terms, yet the resulting dimensionalites are equivalent to thermal spin systems. Physical implications are discussed.
dc.description28 pages, 6 figures; Paper has been amplified with a more detailed discussion of a number of technical issues
dc.identifierhttps://arxiv.org/abs/hep-th/0210076
dc.identifierhttp://arxiv.org/abs/hep-th/0210076
dc.identifierPhys.Rev.D67:085004,2003
dc.identifierdoi:10.1103/PhysRevD.67.085004
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/202787
dc.subjectHigh Energy Physics - Theory
dc.subjectHigh Energy Physics - Phenomenology
dc.titleFractal Theory Space: Spacetime of Noninteger Dimensionality
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