HOME    |    BROWSE    |    SEARCH    |    SUBSCRIPTION   |    SUBMISSION    |    REGISTRATION

Quick Search:
Author: Title/Abstract: Vol./No: Page:
PTP Online Top > Volume 86 (1991) > Number 2
| Next Article >

Prog. Theor. Phys. Vol. 86 No. 2 (1991) pp. 517-545

[ Full Text PDF : FREE ACCESS (1002K) ]

Zweibein Operator Formalism of Two-Dimensional Quantum Gravity

Mitsuo Abe and Noboru Nakanishi

Research Institute for Mathematical Sciences, Kyoto University, Kyoto 606-01

(Received February 1, 1991)

Abstract:

The unitary, manifestly covariant operator formalism of two-dimensional quantum gravity, presented previously, is extended to the zweibein formalism. All the two-dimensional (anti)commutation relations between primary fields are obtained in closed form. The four degrees of freedom of the zweibein are shown to be realized as q-number transformation functions of the general coordinate transformation, the local Lorentz transformation and the Weyl transformation. As the result, the explicit expression for the gravitational extension of the Pauli-Jordan D-function is found in terms of the zweibein. Bosonized operator solutions known in solvable two-dimensional models are extended to the quantum-gravity case through the above q-number transformations.


URL : http://ptp.ipap.jp/link?PTP/86/517/
DOI : 10.1143/PTP.86.517

[ Full Text PDF : FREE ACCESS (1002K) ] Citation:

References:

  1. M. Abe and N. Nakanishi, Int. J. Mod. Phys. A6.
  2. N. Nakanishi and I. Ojima, Covariant Operator Formalism of Gauge Theories and Quantum Gravity (World Scientific, Singapore, 1990), chap. 5.
  3. N. Nakanishi, Prog. Theor. Phys. 62 (1979), 779[PTP].
  4. K. Sato, Preprint EPHOU87, APR003 (Hokkaido).
  5. B. Klaiber, in 1967 Boulder Lecture in Theoretical Physics (Gordon and Breach, New York, 1968), vol. XA, p. 141.
  6. N. Nakanishi, Prog. Theor. Phys. 57 (1977), 269[PTP].
  7. For a review, see the book of Ref. 2), sec. 2.5.
  8. K. Johnson, Nuovo Cim. 20 (1961), 773.
  9. N. Nakanishi, Prog. Theor. Phys. 57 (1977), 580[PTP].
  10. M. Abe and N. Nakanishi, Prog. Theor. Phys. 85 (1991), 391[PTP].
  11. A. M. Polyakov, Mod. Phys. Lett. A2 (1987), 893.

Citing Article(s) :

  1. Progress of Theoretical Physics Vol. 86 No. 5 (1991) pp. 1087-1109 :
    Wightman Functions in Covariant Operator Formalism of Two-Dimensional Quantum Gravity
    Mitsuo Abe and Noboru Nakanishi
  2. Progress of Theoretical Physics Vol. 87 No. 2 (1992) pp. 495-505 :
    Wightman Functions in Covariant Operator Formalism of Two-Dimensional Quantum Gravity. II
    Mitsuo Abe and Noboru Nakanishi
  3. Progress of Theoretical Physics Vol. 87 No. 3 (1992) pp. 757-769 :
    Wightman Functions in Covariant Operator Formalism of Two-Dimensional Quantum Gravity. III
    Mitsuo Abe and Noboru Nakanishi
  4. Progress of Theoretical Physics Vol. 88 No. 5 (1992) pp. 975-991 :
    How to Solve the Covariant Operator Formalism of Gauge Theories and Quantum Gravity in the Heisenberg Picture. I
    Mitsuo Abe and Noboru Nakanishi
  5. Progress of Theoretical Physics Vol. 89 No. 1 (1993) pp. 231-244 :
    How to Solve the Covariant Operator Formalism of Gauge Theories and Quantum Gravity in the Heisenberg Picture. II
    Mitsuo Abe and Noboru Nakanishi
  6. Progress of Theoretical Physics Vol. 89 No. 2 (1993) pp. 501-522 :
    How to Solve the Covariant Operator Formalism of Gauge Theories and Quantum Gravity in the Heisenberg Picture. III
    Mitsuo Abe and Noboru Nakanishi
  7. Progress of Theoretical Physics Vol. 90 No. 3 (1993) pp. 705-716 :
    How to Solve the Covariant Operator Formalism of Gauge Theories and Quantum Gravity in the Heisenberg Picture. IV
    Mitsuo Abe and Noboru Nakanishi
  8. Progress of Theoretical Physics Vol. 90 No. 5 (1993) pp. 1091-1109 :
    New Diagrammatic Method for Quantum Field Theory in the Heisenberg Picture. I
    Mitsuo Abe and Noboru Nakanishi
  9. Progress of Theoretical Physics Vol. 90 No. 6 (1993) pp. 1319-1342 :
    New Diagrammatic Method for Quantum Field Theory in the Heisenberg Picture. II
    Mitsuo Abe and Noboru Nakanishi
  10. Progress of Theoretical Physics Vol. 92 No. 2 (1994) pp. 449-464 :
    New Diagrammatic Method for Quantum Field Theory in the Heisenberg Picture. III
    Mitsuo Abe and Noboru Nakanishi
  11. Progress of Theoretical Physics Vol. 94 No. 4 (1995) pp. 621-635 :
    Operator-Formalism Approach to Two-Dimensional Quantum Gravity in the Lightcone Gauge
    Mitsuo Abe and Noboru Nakanishi
  12. Progress of Theoretical Physics Vol. 96 No. 6 (1996) pp. 1281-1290 :
    Subtlety in the Anomaly Calculation of String Theory in the Harmonic Gauge
    Mitsuo Abe and Noboru Nakanishi
  13. Progress of Theoretical Physics Vol. 100 No. 5 (1998) pp. 1063-1075 :
    Anomaly Problem in a Simple Model Analogous to the Lightcone-Gauge Two-Dimensional Quantum Gravity
    Mitsuo Abe and Noboru Nakanishi
  14. Progress of Theoretical Physics Vol. 111 No. 3 (2004) pp. 301-337 :
    Method for Solving Quantum Field Theory in the Heisenberg Picture
    Noboru Nakanishi
  15. Progress of Theoretical Physics Supplement No.110 (1992) pp. 81-95 :
    Weyl Invariant Formulation of Two-Dimensional Quantum Gravity
    Ki-ichiro Sato

[PTP HOME] [BROWSE] [SEARCH] [SUBSCRIPTION] [SUBMISSION] [REGISTRATION]

Copyright © Progress of Theoretical Physics 2013 All rights reserved.