TY  - BOOK
A1  - Davis, Simon
T1  - Connections and generalized gauge transformation
T3  - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell
Y1  - 2002
SN  - 1437-739X
PB  - Univ.
CY  - Potsdam
ER  - 
TY  - INPR
A1  - Davis, Simon
T1  - Connections and generalized gauge transformations
N2  - The derivation of the standard model from a higher-dimensional action suggests a further study of the fibre bundle formulation of gauge theories to determine the variations in the choice of structure group that are allowed in this geometrical setting. The action of transformations on the projection of fibres to their submanifolds are characteristic of theories with fewer gauge vector bosons, and specific examples are given, which may have phenomenological relevance. The spinor space for the three generations of fermions in the standard model is described algebraically.
T3  - Preprint - (2002) 29 
KW  - bundles
KW  - connections
KW  - fibre coordinates
KW  - parallelizable spheres
KW  - division algebras
KW  - force unification
Y1  - 2002
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26468
ER  - 
TY  - BOOK
A1  - Davis, Simon
T1  - On the absence of large-order divergences in superstring theory
T3  - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell
Y1  - 2002
SN  - 1437-739X
PB  - Univ.
CY  - Potsdam
ER  - 
TY  - INPR
A1  - Davis, Simon
T1  - On the absence of large-order divergences in superstring theory
N2  - The genus-dependence of multi-loop superstring ams is estimated at large orders in perturbation theory using the super-Schottky group parameterization of supermoduli space. Restriction of the integration region to a subset of supermoduli space and a single fundamental domain of the super-modular group suggests an exponential dependence on the genus. Upper bounds for these estimates are obtained for arbitrary N-point superstring scattering amplitudes and are shown to be consistent with exact results obtained for special type II string amplitudes for orbifold or Calabi-Yau compactifications. The genus-dependence is then obtained by considering the effect of the remaining contribution to the superstring amplitudes after the coefficients of the formally divergent parts of the integrals vanish as a result of a sum over spin structures. The introduction of supersymmetry therefore leads to the elimination of large-order divergences in string pertubation theory, a result which is based only on the supersymmetric generalization of the polyakov measure and not the gauge group of the string model.
T3  - Preprint - (2002) 28 
Y1  - 2002
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26452
ER  - 
TY  - BOOK
A1  - Davis, Simon
T1  - On the existence of a non-zero lower bound for the number of goldbach partitions of an even integer
T3  - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell
Y1  - 2002
SN  - 1437-739X
PB  - Univ.
CY  - Potsdam
ER  - 
TY  - INPR
A1  - Davis, Simon
T1  - On the existence of a non-zero lower bound for the number of Goldbach partitions of an even integer
N2  - The Goldbach partitions of an even number greater than 2, given by the sums of two prime addends, form the non-empty set for all integers 2n with 2 ≤ n ≤ 2 × 1014. It will be shown how to determine by the method of induction the existence of a non-zero lower bound for the number of Goldbach partitions of all even integers greater than or equal to 4. The proof depends on contour arguments for complex functions in the unit disk.
T3  - Preprint - (2002) 30 
Y1  - 2002
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26474
ER  - 
TY  - BOOK
A1  - Davis, Simon
T1  - The quantum cosmological wavefunction at very early times for a quadratic gravity theory
T3  - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell
Y1  - 2003
SN  - 1437-739X
PB  - Univ.
CY  - Potsdam
ER  - 
TY  - INPR
A1  - Davis, Simon
T1  - The quantum cosmological wavefunction at very early times for a quadratic gravity theory
N2  - The quantum cosmological wavefunction for a quadratic gravity theory derived from the heterotic string effective action is obtained near the inflationary epoch and during the initial Planck era. Neglecting derivatives with respect to the scalar field, the wavefunction would satisfy a third-order differential equation near the inflationary epoch which has a solution that is singular in the scale factor limit a(t) → 0. When scalar field derivatives are included, a sixth-order differential equation is obtained for the wavefunction and the solution by Mellin transform is regular in the a → 0 limit. It follows that inclusion of the scalar field in the quadratic gravity action is necessary for consistency of the quantum cosmology of the theory at very early times.
T3  - Preprint - (2003) 04 
Y1  - 2003
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26520
ER  -