Philosophy as Cultural Analysis

Myers, Gerald E.; McDermott, John J.; McDonald, Henry

doi:10.2307/2712889

American Quarterly

1987

DOI: 10.2307/2712889

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Philosophy as Cultural Analysis

Gerald E. Myers¹,

John J. McDermott²,

Henry McDonald³

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1996

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“…For solutions expressible in terms of Painlevé transcendents [30] the matrices M j are triangular. The only examples of solutions which are not strictly isomonodromic in the sense that the sum in (3.12) is infinite and that there is an accumulation point of the poles at infinity are the periodic analogs of the axisymmetric static solutions constructed in [31,21]. Evidently, such solutions may be obtained from the N -soliton solutions by a limiting procedure.…”

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confidence: 99%

Isomonodromic quantization of dimensionally reduced gravity

Korotkin¹,

Nicolai²

1996

Nuclear Physics B

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Abstract. We present a detailed account of the isomonodromic quantization of dimensionally reduced Einstein gravity with two commuting Killing vectors. This theory constitutes an integrable "midi-superspace" version of quantum gravity with infinitely many interacting physical degrees of freedom. The canonical treatment is based on the complete separation of variables in the isomonodromic sectors of the model. The Wheeler-DeWitt and diffeomorphism constraints are thereby reduced to the Knizhnik-Zamolodchikov equations for SL(2, R). The physical states are shown to live in a well defined Hilbert space and are manifestly invariant under the full diffeomorphism group. An infinite set of independent observablesà la Dirac exists both at the classical and the quantum level. Using the discrete unitary representations of SL(2, R), we construct explicit quantum states. However, satisfying the additional constraints associated with the coset space SL(2, R)/SO(2) requires solutions based on the principal series representations, which are not yet known. We briefly discuss the possible implications of our results for string theory.

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confidence: 99%

Isomonodromic quantization of dimensionally reduced gravity

Korotkin¹,

Nicolai²

1996

Nuclear Physics B

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Philosophy as Cultural Analysis

Cited by 1 publication

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Isomonodromic quantization of dimensionally reduced gravity

Isomonodromic quantization of dimensionally reduced gravity

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