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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Communications in mathematical physics 66 (1979), S. 197-221 
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract Building upon Kostant's graded manifold theory, we present a new way of introducing spinors into the spacetime manifold, by expanding the algebra of functions on spacetime to a graded algebra. The elements of differential geometry are generalized to accomodate the expanded algebra of functions and in this enriched geometry we find the elements of supersymmetry and of supergravity theory. The geometrical role of the supergravity fields is discussed and a derivation of their transformation rules is given.
    Type of Medium: Electronic Resource
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  • 2
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract A 3+1 formulation of complex Einstein's equation is first obtained on a real 4-manifoldM, topologically σ×R, where σ is an arbitrary 3-manifold. The resulting constraint and evolution equations are then simplified by using variables that capture the (anti-) self dual part of the 4-dimensional Weyl curvature. As a result, to obtain a vacuum self-dual solution, one has just to solve one constraint and one “evolution” equation on a field of triads on σ: $$Div V_i^a = 0 and \dot V_i^a = \varepsilon _{ijk} \left[ {V_j ,V_k } \right]^a , with i \equiv 1,2,3,$$ where Div denotes divergence with respect to a fixed, non-dynamical volume element. If the triad is real, the resulting self-dual metric is real and positive definite. This characterization of self-dual solutions in terms of triads appears to be particularly well suited for analysing the issues of exact integrability of the (anti-) self-dual Einstein system. Finally, although the use of a 3+1 decomposition seems artificial from a strict mathematical viewpoint, as David C. Robinson has recently shown, the resulting triad description is closely related to the hyperkähler geometry that (anti-) self-dual vacuum solutions naturally admit.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Springer
    General relativity and gravitation 16 (1984), S. 205-210 
    ISSN: 1572-9532
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract I conjecture, and show for a large class of cases, that given a spacelike hypersurface on which is an arbitrary distribution of linearized gravitons and matter, the latter satisfying the positive energy condition, the expectation value of the number of events in which a graviton is absorbed by or scattered inelastically from the matter within any future time,t, is always less then the expectation value of the number of gravitons in the initial state (except for a set of initial configurations of measure zero). Consequences of this result are: (1) the impossibility of any system containing gravitational radiation reaching thermal equilibrium in a finite time, (2) the absence of an ultraviolet catastrophe for gravitational radiation, (3) the impossibility of measuring accurately the quantum state of the linearized gravitational field, and (4) the impossibility of constructing a gravitational wave laser.
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  • 4
    Electronic Resource
    Electronic Resource
    Springer
    General relativity and gravitation 17 (1985), S. 1209-1216 
    ISSN: 1572-9532
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract A distribution of virtual black holes in the vacuum will induce modifications in the density of states for small perturbations of gravitational and matter fields. If the virtual black holes fill the volume of a typical spacelike surface then perturbation theory becomes more convergent and may even be finite, depending on how fast the number of virtual black holes increases as their size decreases. For distributions of virtual black holes which are scale invariant the effective dimension of space-time is lowered to a noninteger value less than 4, leading to an interpretation in terms of fractal geometry. In this case general relativity is renormalizable in the 1/N expansion without higher derivative terms. As the Hamiltonian is not modified the theory is stable.
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    Springer
    General relativity and gravitation 17 (1985), S. 417-437 
    ISSN: 1572-9532
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract I show that in linearized general relativity it is impossible to construct a detector by the use of which the quantum state of the linearized gravitational field could be reliably determined. This is because there is no material satisfying the positive energy condition which can serve as a good conductor or absorber of gravitational radiation over a finite range of frequencies. If this property is true of the full theory then one can conclude that a certain proportion of both the energy and information carried by a gravitational wave is irreversibly lost, and that there is a correspondingintrinsic entropy associated with any distribution of gravitational radiation.
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  • 6
    ISSN: 1572-9575
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Three independent arguments are given for the conclusion that the distinction between quantum fluctuations and real statistical fluctuations in the state of a system will not be maintained in a theory that gives a correct description of phenomena in which quantum and gravitational effects are both important. As this distinction is absolute in terms of the orthodox interpretation of the quantum state something in either the interpretation of the quantum state or the interpretation of the thermodynamic state will have to be altered to construct a theory which describes both quantum and gravitational phenomena. I propose that we pursue the simplest possibility, which is to adopt the statistical interpretation of the wave function in which quantum fluctuations are understood to be ordinary statistical fluctuations in an ensemble of individual physical systems.
    Type of Medium: Electronic Resource
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  • 7
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 36 (1995), S. 6417-6455 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Quantum gravity is studied nonperturbatively in the case in which space has a boundary with finite area. A natural set of boundary conditions is studied in the Euclidean signature theory in which the pullback of the curvature to the boundary is self-dual (with a cosmological constant). A Hilbert space which describes all the information accessible by measuring the metric and connection induced in the boundary is constructed and is found to be the direct sum of the state spaces of all SU(2) Chern–Simon theories defined by all choices of punctures and representations on the spatial boundary S. The integer level k of Chern–Simons theory is found to be given by k=6π/G2Λ+α, where Λ is the cosmological constant and α is a CP breaking phase. Using these results, expectation values of observables which are functions of fields on the boundary may be evaluated in closed form. Given these results, it is natural to make the conjecture that the quantum states of the system are completely determined by measurements made on the boundary. One consequence of this is the Bekenstein bound, which says that once the two metric of the boundary has been measured, the subspace of the physical state space that describes the further information that may be obtained about the interior has finite dimension equal to the exponent of the area of the boundary, in Planck units, times a fixed constant. Finally, these results confirm both the categorical-theoretic "ladder of dimensions'' picture of Crane and the holographic hypothesis of Susskind and 't Hooft. © 1995 American Institute of Physics.
    Type of Medium: Electronic Resource
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