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• 1
Electronic Resource
Springer
ISSN: 1432-0916
Source: Springer Online Journal Archives 1860-2000
Topics: Mathematics , Physics
Notes: Abstract The set of allC 2 Lorentz metrics on a non-compact four-manifold is given the Whitney fineC 2 topology. It is shown that this provides the correct framework within which to discuss the global properties of spacetime manifolds in general, and the singularity theorems in particular. The main result is a theorem showing that the Robertson-Walker big bang (global infinite density singularity in the finite past) is stable under sufficiently small, but otherwise arbitrary, finiteC 2 perturbations of the metric tensor.
Type of Medium: Electronic Resource
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• 2
Electronic Resource
Springer
Communications in mathematical physics 55 (1977), S. 179-182
ISSN: 1432-0916
Source: Springer Online Journal Archives 1860-2000
Topics: Mathematics , Physics
Notes: Abstract Elementary group-theoretical considerations show that global solutions to the massless free field equations are functions on the bundle of twistor dyads, rather than the bundle of conformal spin frames. Only in certain degenerate cases may they be thought of as ordinary spinor fields. This is the origin of the “Grgin discontinuity”.
Type of Medium: Electronic Resource
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• 3
Electronic Resource
Springer
Communications in mathematical physics 132 (1990), S. 537-547
ISSN: 1432-0916
Source: Springer Online Journal Archives 1860-2000
Topics: Mathematics , Physics
Notes: Abstract For a particular class of patching matrices onP 3(ℂ), including those for the complex instanton bundles with structure group Sp(k,ℂ) orO(2k,ℂ), we show that the associated Riemann-Hilbert problemG(x, λ)=G−(x, λ)·G + −1 (x, λ) can be generically solved in the factored formG −=φ 1 φ 2.....φ n . IfГ=Г n is the potential generated in the usual way fromG −, and we setψ i =φ 1.....,φ i withψ n =G −, then eachψ i also generates a selfdual gauge potentialΓ i . The potentials are connected via the “dressing transformations” $$\Gamma _\iota = \phi _i^{ - 1} \cdot \Gamma _{\iota - 1} \cdot \phi _i + \phi _i ^{ - 1} D\phi _i$$ of Zakharov-Shabat. The factorization is not unique; it depends on the (arbitrary) ordering of the poles of the patching matrix.
Type of Medium: Electronic Resource
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