scholarly journals Zweibein Operator Formalism of Two-Dimensional Quantum Gravity

1991 ◽  
Vol 86 (2) ◽  
pp. 517-545
Author(s):  
M. Abe ◽  
N. Nakanishi
Keyword(s):  
Quantum Gravity ◽  
Two Dimensional ◽  
Operator Formalism

scholarly journals HUGE SPACE-DEPENDENT SYMMETRY IN THE LIGHTCONE GAUGE TWO-DIMENSIONAL QUANTUM GRAVITY

1996 ◽  
Vol 11 (15) ◽  
pp. 2623-2642 ◽  
Author(s):  
MITSUO ABE ◽  
NOBORU NAKANISHI
Keyword(s):  
Quantum Gravity ◽  
Current Algebra ◽  
Symmetry Algebra ◽  
Local Version ◽  
Two Dimensional ◽  
Operator Formalism ◽  
Canonical Operator ◽  
Coordinate Invariance

The lightcone gauge two-dimensional quantum gravity, i.e. the local version of Polyakov’s “induced” quantum gravity, is analyzed in the canonical operator formalism. An extremely huge x+-dependent symmetry algebra is found to exist in this model. Both Polyakov’s SL (2, R) current algebra and residual general coordinate invariance are very very tiny subalgebras of it.

COVARIANT OPERATOR FORMALISM OF TWO-DIMENSIONAL TOPOLOGICAL GRAVITY

1992 ◽  
Vol 07 (13) ◽  
pp. 3105-3131
Author(s):  
NORIAKI IKEDA
Keyword(s):  
Quantum Gravity ◽  
Two Dimensional ◽  
Operator Formalism ◽  
Canonical Operator ◽  
Covariant Operator ◽  
Gauge Fixing ◽  
Topological Gravity

The manifestly covariant canonical operator formalism of two-dimensional topological gravity is formulated. Its unitarity is confirmed by means of constructing the Kugo–Ojima's quartets. A number of new symmetries are found by adopting a particular gauge fixing condition. These symmetries correspond to the "choral symmetry" generated by the 4N-dimensional Poincaré-like superalgebra in the ordinary N-dimensional quantum gravity.

scholarly journals ON THE EXACT OPERATOR FORMALISM OF TWO-DIMENSIONAL LIOUVILLE QUANTUM GRAVITY IN MINKOWSKI SPACE-TIME

1994 ◽  
Vol 09 (05) ◽  
pp. 667-710 ◽  
Author(s):  
YOICHI KAZAMA ◽  
HERMANN NICOLAI
Keyword(s):  
Quantum Gravity ◽  
Minkowski Space ◽  
Central Charge ◽  
Free Field ◽  
Space Time ◽  
Cosmological Term ◽  
Two Dimensional ◽  
Operator Formalism ◽  
Minkowski Space Time ◽  
Exponential Operator

A detailed re-examination is made of the exact operator formalism of two-dimensional Liouville quantum gravity in Minkowski space-time with the cosmological term fully taken into account. Making use of the canonical mapping from the interacting Liouville field into a free field, we focus on the problem of how the Liouville exponential operator should be properly defined. In particular, the condition of mutual locality among the exponential operators is carefully analyzed, and a new solution, which is neither smoothly connected nor relatively local to the existing solution, is found. Our analysis indicates that, in Minkowski space-time, coupling gravity to matter with central charge d<1 is problematical. For d=1, our new solution appears to be the appropriate one; for this value of d, we demonstrate that the operator equation of motion is satisfied to all orders in the cosmological constant with a certain regularization. As an application of the formalism, an attempt is made to study how the basic generators of the ground ring get modified due to the inclusion of the cosmological term. Our investigation, although incomplete, suggests that in terms of the canonically mapped free field the ground ring is not modified.

PERTURBATIVE RECONFIRMATION OF THE EXACT COVARIANT SOLUTION TO THE TWO-DIMENSIONAL QUANTUM GRAVITY

1992 ◽  
Vol 07 (25) ◽  
pp. 6405-6420 ◽  
Author(s):  
MITSUO ABE ◽  
NOBORU NAKANISHI
Keyword(s):  
Exact Solution ◽  
Perturbation Theory ◽  
Quantum Gravity ◽  
Finite Number ◽  
Two Dimensional ◽  
Operator Formalism ◽  
Perturbative Approach ◽  
Covariant Operator ◽  
Feynman Graphs ◽  
Field Redefinition

The validity of the exact solution to the covariant operator formalism of two-dimensional quantum gravity is reconfirmed by means of the conventional perturbation theory. Only a finite number of Feynman graphs are encountered, yet, the perturbative approach is much more complicated than the exact method. A unitarized, covariantized Polyakov theory, which has an infinite number of Feynman graphs, is obtained from the above result by a simple field redefinition.

UNITARY THEORY OF TWO-DIMENSIONAL QUANTUM GRAVITY AND ITS EXACT COVARIANT OPERATOR SOLUTION

1991 ◽  
Vol 06 (22) ◽  
pp. 3955-3971 ◽  
Author(s):  
MITSUO ABE ◽  
NOBORU NAKANISHI
Keyword(s):  
Quantum Gravity ◽  
Two Dimensional ◽  
Operator Formalism ◽  
Unitary Theory ◽  
Operator Solution ◽  
Canonical Operator ◽  
Weyl Invariance ◽  
Covariant Operator ◽  
Gauge Fixing

The manifestly covariant canonical operator formalism of two-dimensional quantum gravity is formulated on the basis of Sato’s gauge-fixing of the Weyl invariance. The unitarity problem, due to ghost-counting mismatch, is resolved by making the gravitational FP ghosts also play the role of the Weyl FP ghosts. All two-dimensional (anti)commutators between fundamental fields are explicitly obtained.

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