Wightman Functions in Covariant Operator Formalism of Two-Dimensional Quantum Gravity

1991 ◽  
Vol 86 (5) ◽  
pp. 1087-1109 ◽  
Author(s):  
M. Abe ◽  
N. Nakanishi
Keyword(s):  
Quantum Gravity ◽  
Two Dimensional ◽  
Operator Formalism ◽  
Covariant Operator ◽  
Wightman Functions

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.

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.

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.

scholarly journals CONSTRUCTION OF AN IDENTICALLY NILPOTENT BRS CHARGE IN THE KATO–OGAWA STRING THEORY

1999 ◽  
Vol 14 (09) ◽  
pp. 1357-1377 ◽  
Author(s):  
MITSUO ABE ◽  
NOBORU NAKANISHI
Keyword(s):  
Field Equation ◽  
String Theory ◽  
Quantum Gravity ◽  
Bosonic Strings ◽  
Open String ◽  
Indefinite Metric ◽  
Two Dimensional ◽  
Conformal Gauge ◽  
Wightman Functions ◽  
Artificial Introduction

In previous work, the conformal-gauge two-dimensional quantum gravity in the BRS formalism has been solved completely in terms of Wightman functions. In the present paper, this result is extended to the closed and open bosonic strings of finite length; the open-string case is nothing but the Kato–Ogawa string theory. The field-equation anomaly found previously, which means a slight violation of a field equation at the level of Wightman functions, remains existent in the finite-string cases. By using this fact, a BRS charge nilpotent even for D≠26 is explicitly constructed in the framework of the Kato–Ogawa string theory. The FP-ghost vacuum structure of the Kato–Ogawa theory is made more transparent; the appearance of half-integral ghost numbers and the artificial introduction of an indefinite metric are avoided.

Sign in / Sign up

Export Citation Format

Share Document