scholarly journals IMPROVED DIRAC QUANTIZATION OF A FREE PARTICLE

2000 ◽  
Vol 15 (31) ◽  
pp. 1915-1922 ◽  
Author(s):  
SOON-TAE HONG ◽  
WON TAE KIM ◽  
YOUNG-JAI PARK
Keyword(s):  
Energy Spectrum ◽  
Free Particle ◽  
Dimensional Sphere ◽  
Class Constraint ◽  
Dirac Quantization ◽  
Physical Consequences

In the framework of Dirac quantization with second-class constraints, a free particle moving on the surface of a (d-1)-dimensional sphere has an ambiguity in the energy spectrum due to the arbitrary shift of canonical momenta. We explicitly show that this spectrum obtained by the Dirac method is consistent with the result of the Batalin–Fradkin–Tyutin formalism, which is an improved Dirac method, at the level of the first-class constraint by fixing the ambiguity, and discuss its physical consequences.

scholarly journals Proper Dirac quantization of a free particle on a D-dimensional sphere

1997 ◽  
Vol 232 (5) ◽  
pp. 327-332 ◽  
Author(s):  
Hagen Kleinert ◽  
Sergei V. Shabanov
Keyword(s):  
Free Particle ◽  
Dimensional Sphere ◽  
Dirac Quantization

scholarly journals BRST SYMMETRIES IN FREE PARTICLE SYSTEM ON TORIC GEOMETRY

2005 ◽  
Vol 20 (21) ◽  
pp. 1577-1588 ◽  
Author(s):  
SOON-TAE HONG
Keyword(s):  
Energy Spectrum ◽  
Particle System ◽  
Free Particle ◽  
Particle Dynamics ◽  
Toric Geometry ◽  
Symplectic Structures

We study a free particle system residing on a torus to investigate its Becci–Rouet–Stora–Tyutin symmetries associated with its Stückelberg coordinates, ghosts and anti-ghosts. By exploiting zeibein frame on the toric geometry, we evaluate energy spectrum of the system to describe the particle dynamics. We also investigate symplectic structures involved in the free particle system on the torus.

The Schrödinger equation: total interaction as perturbation

1982 ◽  
Vol 380 (1779) ◽  
pp. 489-494 ◽  
Keyword(s):  
Energy Spectrum ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Eigenvalue Problems ◽  
Free Particle ◽  
Analytic Approximation ◽  
Binding Interaction ◽  
General Applicability ◽  
Total Interaction

The quantization of the energy spectrum of a free particle in the presence of a binding interaction is reconsidered here. These considerations form the basis of a simple analytic approximation of general applicability to eigenvalue problems.

DISCRETIZED BRST TRANSFORMATIONS AND QUANTUM MECHANICAL POTENTIAL OF A FREE PARTICLE ON SD

2005 ◽  
Vol 20 (09) ◽  
pp. 699-706 ◽  
Author(s):  
KATSUTARO SHIMIZU
Keyword(s):  
Path Integral ◽  
Free Particle ◽  
Quantum Mechanical ◽  
Dimensional Sphere ◽  
Brst Transformation ◽  
Canonical Variables

We evaluated a quantum mechanical potential of a free particle on D-dimensional sphere. This system has the second-class constraints. We change the second-class constraints into first-class ones with new canonical variables. A BRST transformation is induced by the first-class constraints and is discretized. A discretized BRST invariant path integral is considered and the quantum mechanical potential is evaluated as R/12.

scholarly journals BRST INVARIANT CP1 MODEL THROUGH IMPROVED DIRAC QUANTIZATION

2001 ◽  
Vol 16 (21) ◽  
pp. 1361-1376 ◽  
Author(s):  
SOON-TAE HONG ◽  
YOUNG-JAI PARK ◽  
KUNIHARU KUBODERA ◽  
FRED MYHRER
Keyword(s):  
Energy Spectrum ◽  
Path Integral ◽  
Sigma Model ◽  
Nonlinear Sigma Model ◽  
Rigid Rotator ◽  
Dirac Quantization ◽  
Collective Coordinate ◽  
Integral Procedure ◽  
Physical Fields ◽  
Invariant Gauge

The Batalin–Fradkin–Tyutin (BFT) scheme, which is an improved version of Dirac quantization, is applied to the CP1 model, and the compact form of a nontrivial first-class Hamiltonian is directly obtained by introducing the BFT physical fields. We also derive a BRST-invariant gauge fixed Lagrangian through the standard path-integral procedure. Furthermore, performing collective coordinate quantization we obtain energy spectrum of rigid rotator in the CP1 model. Exploiting the Hopf bundle, we also show that the CP1 model is exactly equivalent to the O(3) nonlinear sigma model at the canonical level.

scholarly journals DIRAC QUANTIZATION OF RESTRICTED QCD

2007 ◽  
Vol 22 (37) ◽  
pp. 2799-2813 ◽  
Author(s):  
Y. M. CHO ◽  
SOON-TAE HONG ◽  
J. H. KIM ◽  
YOUNG-JAI PARK
Keyword(s):  
Gauge Theory ◽  
Brst Symmetry ◽  
Quantization Scheme ◽  
Class Constraint ◽  
Constrained System ◽  
Constraint System ◽  
Dirac Quantization ◽  
As If

We discuss the quantization of the restricted gauge theory of SU(2) QCD regarding it as a second-class constraint system, and construct the BRST symmetry of the constrained system in the framework of the improved Dirac quantization scheme. Our analysis tells that one could efficiently quantize the restricted QCD under the BRST symmetry as if it is a first-class constraint system.

scholarly journals DIRAC QUANTIZATION OF FREE MOTION ON CURVED SURFACES

2006 ◽  
Vol 03 (04) ◽  
pp. 655-666 ◽  
Author(s):  
ALEXEY V. GOLOVNEV
Keyword(s):  
Particle Motion ◽  
Free Particle ◽  
Quantum Potential ◽  
Free Motion ◽  
Curved Surfaces ◽  
Dirac Quantization ◽  
Operator Realization ◽  
Natural Way

We give an explicit operator realization of Dirac quantization of free particle motion on a surface of codimension 1. It is shown that the Dirac recipe is ambiguous and a natural way of fixing this problem is proposed. We also introduce a modification of Dirac procedure which yields zero quantum potential. Some problems of Abelian conversion quantization are pointed out.

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