HAMILTON–JACOBI QUANTIZATION OF TWO-DIMENSIONAL GRAVITY WITH TORSION

2004 ◽  
Vol 19 (02) ◽  
pp. 151-157 ◽  
Author(s):  
SAMI I. MUSLIH
Keyword(s):  
Phase Space ◽  
Differential Equations ◽  
Path Integral ◽  
Equations Of Motion ◽  
Two Dimensional ◽  
Path Integral Quantization ◽  
Action Integral ◽  
Total Differential ◽  
Jacobi Formalism ◽  
Dimensional Gravity

Two-dimensional gravity with torsion is investigated using the Hamilton–Jacobi formalism. The equations of motion and the action integral are obtained as total differential equations in many variables. The integrabilty conditions, lead us to obtain the path integral quantization as an integration over the canonical phase-space coordinates.

PATH INTEGRAL QUANTIZATION OF SUPERSTRING

2010 ◽  
Vol 25 (02) ◽  
pp. 135-141
Author(s):  
H. A. ELEGLA ◽  
N. I. FARAHAT
Keyword(s):  
Phase Space ◽  
Differential Equations ◽  
Path Integral ◽  
Equations Of Motion ◽  
Singular System ◽  
Constrained Systems ◽  
Classical Structure ◽  
Path Integral Quantization ◽  
Total Differential

Motivated by the Hamilton–Jacobi approach of constrained systems, we analyze the classical structure of a four-dimensional superstring. The equations of motion for a singular system are obtained as total differential equations in many variables. The path integral quantization based on Hamilton–Jacobi approach is applied to quantize the system, and the integration is taken over the canonical phase space coordinates.

INTEGRABILITY AND ACTION FUNCTION IN MULTI-HAMILTONIAN SYSTEMS

2004 ◽  
Vol 19 (11) ◽  
pp. 863-870 ◽  
Author(s):  
S. I. MUSLIH
Keyword(s):  
Differential Equations ◽  
Hamiltonian Systems ◽  
Equations Of Motion ◽  
Integral Function ◽  
Jacobi Method ◽  
Action Function ◽  
Action Integral ◽  
Method Integration ◽  
Total Differential

Multi-Hamiltonian systems are investigated by using the Hamilton–Jacobi method. Integration of a set of total differential equations which includes the equations of motion and the action integral function is discussed. It is shown that this set is integrable if and only if the total variations of the Hamiltonians vanish. Two examples are studied.

THE CANONICAL PATH INTEGRAL QUANTIZATION OF CHIRAL SCHWINGER MODEL

2003 ◽  
Vol 18 (17) ◽  
pp. 1187-1196 ◽  
Author(s):  
S. I. MUSLIH
Keyword(s):  
Differential Equations ◽  
Path Integral ◽  
Integral Method ◽  
Equation Of Motion ◽  
Action Function ◽  
Schwinger Model ◽  
Integrability Conditions ◽  
Total Differential ◽  
Jacobi Formalism ◽  
Path Integral Method

We quantize the chiral Schwinger model by using the Hamilton–Jacobi formalism. We show that one can obtain the integrable set of equation of motion and the action function by using the integrability conditions of total differential equations and without any need to introduce unphysical auxiliary fields. The path integral for this model is obtained by using the canonical path integral method.

EQUIVALENCE OF TWO-DIMENSIONAL GRAVITIES

1990 ◽  
Vol 05 (16) ◽  
pp. 1251-1258 ◽  
Author(s):  
NOUREDDINE MOHAMMEDI
Keyword(s):  
Gauge Theory ◽  
Explicit Solution ◽  
Light Cone ◽  
Equations Of Motion ◽  
Two Dimensional ◽  
Induced Gravity ◽  
Light Cone Gauge ◽  
Dimensional Gravity ◽  
The Relationship ◽  
Chern Simons

We find the relationship between the Jackiw-Teitelboim model of two-dimensional gravity and the SL (2, R) induced gravity. These are shown to be related to a two-dimensional gauge theory obtained by dimensionally reducing the Chern-Simons action of the 2+1 dimensional gravity. We present an explicit solution to the equations of motion of the auxiliary field of the Jackiw-Teitelboim model in the light-cone gauge. A renormalization of the cosmological constant is also given.

QUANTIZATION OF MECHANICAL SYSTEMS WITH FRACTIONAL DERIVATIVES

2005 ◽  
Vol 20 (27) ◽  
pp. 2095-2099 ◽  
Author(s):  
SAMI I. MUSLIH ◽  
EQAB M. RABEI
Keyword(s):  
Phase Space ◽  
Path Integral ◽  
Fractional Derivatives ◽  
Mechanical Systems ◽  
Path Integral Quantization

In this paper, the mechanical systems with fractional derivatives are studied by using Riewe's formalism. The path integral quantization of these systems is constructed as an integration over the canonical phase space coordinated. An example is shown.

AN INTEGRABLE MODEL WITH SOLITON SOLUTIONS WHICH HAVE APPLICATIONS TO TWO-DIMENSIONAL GRAVITY

2005 ◽  
Vol 20 (07) ◽  
pp. 1503-1514 ◽  
Author(s):  
PAUL BRACKEN
Keyword(s):  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Integrable Model ◽  
Soliton Solutions ◽  
Integrable Equation ◽  
Two Dimensions ◽  
Spin Connection ◽  
Two Dimensional ◽  
Dimensional Gravity ◽  
Chern Simons

The equations of motion for a theory described by a Chern–Simons type of action in two dimensions are obtained and investigated. The equation for the classical, continuous Heisenberg model is used as a form of gauge constraint to obtain a result which provides a completely integrable dynamics and which partially fixes the gauge degrees of freedom. Under a particular form of the spin connection, an integrable equation which can be analytically extended to a form of the nonlinear Schrödinger equation is obtained. Some explicit solutions are presented, and in particular a soliton solution is shown to lead to an integrable two-dimensional model of gravity.

scholarly journals Path Integral Quantization of Regular Lagrangian

2018 ◽  
Vol 10 (1) ◽  
pp. 9
Author(s):  
Ola A. Jarabah
Keyword(s):  
Phase Space ◽  
Path Integral ◽  
Integral Method ◽  
Separation Of Variables ◽  
Integral Formulation ◽  
Path Integral Formulation ◽  
Jacobi Function ◽  
Path Integral Quantization ◽  
Separation Of Variables Method ◽  
Path Integral Method

Path integral formulation based on the canonical method is discussed. The Hamilton Jacobi function for regular Lagrangian is obtained using separation of variables method. This function is used to quantize regular systems using path integral method. The path integral is obtained as integration over the canonical phase space coordinates. One illustrative example is considered to demonstrate the application of our formalism.

Path integral for (2+1)-dimensional Shape Dynamics

2015 ◽  
Vol 30 (12) ◽  
pp. 1550057
Author(s):  
A. González ◽  
H. Ocampo
Keyword(s):  
General Relativity ◽  
Phase Space ◽  
Path Integral ◽  
York Time ◽  
Path Integral Quantization ◽  
Shape Dynamics ◽  
Gauge Fixing ◽  
Dimensional Shape

We studied the path integral quantization for the Shape Dynamics formulation of General Relativity in the 2+1 torus universe. We show that the Shape Dynamics path integral on the reduced phase space is equivalent with the previous results obtained for the ADM 2+1 gravity and we found that the Shape Dynamics Hamiltonian allows us to establish a straightforward relation between reduced systems in the (τ, V)-form and the τ-form through the York time gauge fixing.

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