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  • Articles  (4)
  • De Sitter spacetime  (1)
  • Key words: Symmetric game, stable core, lower boundary, specified vectors  (1)
  • Minisuperspace  (1)
  • Moyal–Weyl algebra  (1)
  • 2000-2004  (4)
  • 1970-1974
  • 1965-1969
  • 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
    A Quantization on Riemann Surfaces with Projective Structure (2000)
    Springer
    Letters in mathematical physics 54 (2000), S. 73-82 
    Details
    ISSN: 1573-0530
    Keywords: projective structure ; symplectic structure ; quantization ; Moyal–Weyl algebra
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract Let X be a Riemann surface equipped with a projective structure. Let $$\mathcal{L}$$ be a square-root of the holomorphic cotangent bundle K X . Consider the symplectic form on the complement of the zero section of $$\mathcal{L}$$ obtained by pulling back the symplectic form on K X using the map ν ↦ ν⊗2. We show that this symplectic form admits a natural quantization. This quantization also gives a quantization of the complement of the zero section in K X equipped with the natural symplectic form.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1007650202446
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  • 3
    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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  • 4
    Electronic Resource
    Electronic Resource
    The Complex Time WKB Approximation and Particle Production (2000)
    Springer
    General relativity and gravitation 32 (2000), S. 53-77 
    Details
    ISSN: 1572-9532
    Keywords: De Sitter spacetime ; particle production
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The complex time WKB (CWKB) approximation has been an effective technique to understand particle production in curved as well as in flat spacetime. Earlier we obtained the standard results on particle production in time-dependent gauge in various curved spacetime, using the method of CWKB. In the present work we generalize the technique of CWKB to the equivalent problems in space-dependent gauge. Using CWKB, we first obtain the gauge invariant result for particle production in Minkowski spacetime in a strong electric field. We then carry out particle production in de Sitter spacetime in space dependent gauge and obtain the same result that we obtained earlier in time dependent gauge. This ensures the gauge invariant description inherent in CWKB. The results obtained for de Sitter spacetime have an obvious extension to particle production in black hole spacetime. It is found that the origin of the Planckian spectrum is due to repeated reflections between the turning points. As mentioned in earlier work, it is now explicitly shown that particle production is accompanied by rotation of currents.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1001896416269
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