State vectors in higher dimensional gravity with kinematic quantum numbers of quarks and leptons

Friedman, J.L.; Higuchi, A.

doi:10.1016/0550-3213(90)90358-K

State vectors in higher dimensional gravity with kinematic quantum numbers of quarks and leptons

1990

25 pages

Published in:

Nucl.Phys.B 339 (1990) 491-515

Published: 1990

DOI:

10.1016/0550-3213(90)90358-K

View in:

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Abstract: (Elsevier)

We examine the question of whether fundamental fermions can be regarded as topological solitons (geons) of a theory of pure quantum gravity in n + 4 dimensions. In particular, we consider the quantum gravitational field for ( n + 4)-dimensional space-times which have asymptotic Kaluza-Klein behavior: asymptotic topology of the form R 4 × G/H and a metric that is asymptotically the direct sum of the Minkowski metric on R 4 and the natural symmetric metric on G/H. We argue that if there is a nonsingular theory of pure quantum gravity (a theory that, below Planck energy, involves only the space-time metric), then there are stable ground states with the kinematical quantum numbers of fundamental fermions: that is, states which have spin 1 2 and belong to the fundamental representation of G . Multi-valued representations of the asymptotic symmetry group can arise from diffeomorphisms (diffeos) of the ( n + 3)-dimensional space that are not isotopic to the identity. In a path integral approach, the creation of fundamental fermions (topological geons) requires a space-time in which the topology of space-like hypersurfaces changes and in which the relevant diffeos on the final ( n + 3)-space (containing the geons) are not extendible to diffeos of the ( n + 4)-space-time. We prove that such pair-creation geometries occur in a lorentzian as well as euclidean framework and that the diffeos are not extendible.

quantum gravity: higher-dimensional
space-time
fermion: model
field equations: soliton
group theory: representation
path integral
fermion: mirror particle
quantum number
Kaluza-Klein model
postulated particle: geon

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