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.

EXACT SOLUTION OF TWO-DIMENSIONAL GRAVITY VIA ANALYTIC CONTINUATION OF MATRIX MODEL

1991 ◽  
Vol 06 (30) ◽  
pp. 2749-2756 ◽  
Author(s):  
P. G. SILVESTROV ◽  
A. S. YELKHOVSKY
Keyword(s):  
Exact Solution ◽  
Perturbation Theory ◽  
Quantum Gravity ◽  
Analytic Continuation ◽  
Matrix Model ◽  
Recent Progress ◽  
Two Dimensional ◽  
Dimensional Gravity

We discuss recent progress in the formulation and solutions of two-dimensional quantum gravity beyond the perturbation theory.

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.

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.

scholarly journals EXACT SOLUTIONS TO THE TWO-DIMENSIONAL BF AND YANG–MILLS THEORIES IN THE LIGHT-CONE GAUGE

2002 ◽  
Vol 17 (11) ◽  
pp. 1491-1502 ◽  
Author(s):  
MITSUO ABE ◽  
NOBORU NAKANISHI
Keyword(s):  
Exact Solution ◽  
Quantum Gravity ◽  
Light Cone ◽  
Lagrangian Density ◽  
Critical Dimension ◽  
Two Dimensional ◽  
Light Cone Gauge ◽  
Yang Mills ◽  
Bf Theory ◽  
Conformal Gauge

It is shown that the BRS (= Becchi–Rouet–Stora)-formulated two-dimensional BF theory in the light-cone gauge (coupled with chiral Dirac fields) is solved very easily in the Heisenberg picture. The structure of the exact solution is very similar to that of the BRS-formulated two-dimensional quantum gravity in the conformal gauge. In particular, the BRS Noether charge has anomaly. Based on this fact, a criticism is made on the reasoning of Kato and Ogawa, who derived the critical dimension D=26 of string theory on the basis of the anomaly of the BRS Noether charge. By adding the [Formula: see text] term to the BF-theory Lagrangian density, the exact solution to the two-dimensional Yang–Mills theory is also obtained.

NONRENORMALIZABILITY MAY BE SUPERFICIAL IN THE COVARIANT FORMALISM OF QUANTUM GRAVITY

1995 ◽  
Vol 10 (21) ◽  
pp. 1501-1506 ◽  
Author(s):  
MITSUO ABE ◽  
NOBORU NAKANISHI
Keyword(s):  
Perturbation Theory ◽  
Quantum Gravity ◽  
Ad Hoc ◽  
Einstein Gravity ◽  
Gravity Theory ◽  
Usual Sense ◽  
Covariant Formalism ◽  
Perturbative Approach

It is pointed out that the nonrenormalizability of quantum Einstein gravity may be caused by the inadequacy of the conventional perturbative approach. It is more reasonable to reconsider the problem in the light of a newly proposed perturbative scheme, which is free of the ad hoc assumption on which the conventional perturbation theory is based. It is explicitly shown that there is a gravity-theory example which is nonrenormalizable in the usual sense but completely finite if the new perturbative scheme is applied.

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