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  • 1
    Electronic Resource
    Electronic Resource
    Quantum Gravity Equation In Schrödinger Form In Minisuperspace Description (2000)
    Springer
    General relativity and gravitation 32 (2000), S. 2167-2187 
    Details
    ISSN: 1572-9532
    Keywords: quantum Cosmology ; Quantum Gravity ; Time ; Minisuperspace ; Wavefunction of the Universe PACS No. - 04.60, 98.80 Hw
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We start from the classical Hamiltonian constraint of general relativity to obtain the Einstein–Hamiltonian–Jacobi equation. We obtain a time parameter prescription demanding that geometry itself determines the time, not the matter field, such that the time so defined being equivalent to the time that enters into the Schrödinger equation. Using a semiclassical approximation we obtain an equation for quantum gravity in Schrödinger form containing time. We restrict ourselves to a minisuperspace description. Unlike matter field equation our equation is equivalent to the Wheeler–DeWitt equation in the sense that our solutions reproduce also the wavefunction of the Wheeler–DeWitt equation provided one evaluates the normalization constant according to the wormhole dominance proposal recently proposed by us.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1001902620253
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  • 2
    Electronic Resource
    Electronic Resource
    Stability and largeness of core for symmetric games (2000)
    Springer
    International journal of game theory 29 (2000), S. 11-22 
    Details
    ISSN: 1432-1270
    Keywords: Key words: Symmetric game, stable core, lower boundary, specified vectors
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract. Largeness of the core is sufficient for stability of the core. In general the necessity is not known. In this paper we answer affirmatively the necessity for symmetric games. We also prove its equivalence to n specified vectors being imputations and also to the convexity of the lower boundary of the set of all acceptable pay-off vectors of the game. In this paper we establish the equivalence of a condition given by Shapley to the newly evolved condition, thereby give an alternate proof to Shapley’s condition.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s001820050002
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