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.

CONDITIONALLY EXACTLY SOLVABLE SINGULAR EVEN POWER POTENTIAL IN SUPERSYMMETRIC QUANTUM MECHANICS

2002 ◽  
Vol 17 (21) ◽  
pp. 1367-1375 ◽  
Author(s):  
BARNALI CHAKRABARTI ◽  
TAPAN KUMAR DAS
Keyword(s):  
Wave Function ◽  
Quantum Mechanics ◽  
Riccati Equation ◽  
Schrodinger Equation ◽  
Supersymmetric Quantum Mechanics ◽  
New Technique ◽  
Body System ◽  
Operator Formalism ◽  
Shape Invariance ◽  
Exactly Solvable

We solve strongly singular even power potential with inverse quadratic, inverse quartic and inverse sextic terms, using superpotential ansatz technique. We show that our new technique is very powerful and simple compared to traditional wave function ansatz technique. We also point out conditional shape invariance as the underlying symmetry to get conditional exactness. We also generalize the case for two-body Hamiltonian and propose an alternative way to solve Riccati equation instead of solving Schrödinger equation. We present operator formalism which is rather powerful. We also discuss the problem encountered in generalizing the potential for an N-body system.

A MICROSCOPIC DERIVATION OF STOCHASTIC DIFFERENTIAL EQUATIONS

1996 ◽  
Vol 10 (13n14) ◽  
pp. 1585-1597
Author(s):  
TOSHIHICO ARIMITSU
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Quantum Systems ◽  
The Other ◽  
Operator Formalism ◽  
Canonical Operator ◽  
Thermo Field Dynamics ◽  
Microscopic Derivation ◽  
Non Equilibrium

With the help of the formulation of Non-Equilibrium Thermo Field Dynamics, constructed is a unified canonical operator formalism for the quantum stochastic differential equations. In the course of its construction, it is found that there are at least two formulations, i.e. one is non-hermitian and the other is hermitian. Having been settled the framework which should be satisfied by the quantum stochastic differential equations, performed is a microscopic derivation of these stochastic differential equations by extending the projector methods. This investigation may open a new field for quantum systems in order to understand the deeper meaning of dissipation.

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.

Time in Quantum Mechanics

2011 ◽  
Author(s):  
Jan Hilgevoord ◽  
David Atkinson
Keyword(s):  
Quantum Mechanics ◽  
Quantum Theory ◽  
Uncertainty Relation ◽  
Classical Mechanics ◽  
Special Problem ◽  
Uncertainty Relations ◽  
Operator Formalism ◽  
Heisenberg Uncertainty ◽  
Time In Quantum Mechanics ◽  
Time Operators

Unlike classical mechanics, quantum mechanics assumes the famous Heisenberg uncertainty relations. One of these concerns time: the energy–time uncertainty relation. Unlike the canonical position–momentum uncertainty relation, the energy–time relation is not reflected in the operator formalism of quantum theory. Indeed, it is often said and taken as problematic that there is not a so-called “time operator” in quantum theory. This chapter sheds light on these questions and others, including the absorbing matter of whether quantum mechanics allows for the existence of ideal clocks. The second section notes that quantum mechanics does not involve a special problem for time, and that there is no fundamental asymmetry between space and time in quantum mechanics over and above the asymmetry which already exists in classical physics. The third section studies time operators in detail. The fourth section discusses various uncertainty relations involving time.

COVARIANT OPERATOR FORMALISM OF TWO-DIMENSIONAL TOPOLOGICAL GRAVITY II

1992 ◽  
Vol 07 (02) ◽  
pp. 131-145
Author(s):  
NORIAKI IKEDA
Keyword(s):  
Lagrangian Density ◽  
Two Dimensional ◽  
Operator Formalism ◽  
Canonical Operator ◽  
Covariant Operator ◽  
Gauge Fixing ◽  
Topological Gravity

Zweibein formalism of two-dimensional topological gravity is formulated in the framework of the manifestly covariant canonical operator formalism. By adopting the new gauge fixing condition, we extend the symmetries of the Lagrangian density, generated by the modified Poincaré-like superalgebra. The intrinsic topological BRS transformation introduced by the previous paper is still the symmetry of the theory.

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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