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.

Free particle dynamics of negative ions in the mechanical vacuum of He II

1982 ◽  
Vol 89 (8) ◽  
pp. 414-416 ◽  
Author(s):  
T. Ellis ◽  
P.V.E. McClintock
Keyword(s):  
Free Particle ◽  
Negative Ions ◽  
Particle Dynamics

scholarly journals Klein tunneling in carbon nanostructures: A free-particle dynamics in disguise

2011 ◽  
Vol 83 (4) ◽  
Author(s):  
Vít Jakubský ◽  
Luis-Miguel Nieto ◽  
Mikhail S. Plyushchay
Keyword(s):  
Carbon Nanostructures ◽  
Free Particle ◽  
Particle Dynamics ◽  
Klein Tunneling

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.

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.

scholarly journals The Quantum Black Hole as a Gravitational Hydrogen Atom

2019 ◽  
Author(s):  
Christian Corda ◽  
Fabiano Feleppa
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Energy Spectrum ◽  
Hydrogen Atom ◽  
Gravitational Potential ◽  
Particle System ◽  
Energy Levels ◽  
Planck Scale ◽  
Dinger Equation ◽  
The One

In this paper only one basic assumption has been made: if we try to describe black holes, their behavior should be understood in the same language as the one we use for particles; black holes should be treated just like atoms. They must be quantum forms of matter, moving in accordance with Schrödinger equations just like everything else. In particular, Rosen’s quantization approach to the gravitational collapse is applied in the simple case of a pressureless “star of dust” by finding the gravitational potential, the Schrödinger equation and the solution for the collapse’s energy levels. By applying the constraints for a Schwarzschild black hole (BH) and by using the concept of BH effective state, previously introduced by one of the authors (CC), the BH quantum gravitational potential, Schrödinger equation and the BH energy spectrum are found. Remarkably, such an energy spectrum is in agreement (in its absolute value) with the one which was conjectured by Bekenstein in 1974 and consistent with other ones in the literature. This approach also permits to find an interesting quantum representation of the Schwarzschild BH ground state at the Planck scale. Moreover, two fundamental issues about black hole quantum physics are addressed by this model: the area quantization and the singularity resolution. As regards the former, a result similar to the one obtained by Bekenstein, but with a different coefficient, has been found. About the latter, it is shown that the traditional classical singularity in the core of the Schwarzschild BH is replaced, in a full quantum treatment, by a two-particle system where the two components strongly interact with each other via a quantum gravitational potential. The two-particle system seems to be non-singular from the quantum point of view and is analogous to the hydrogen atom because it consists of a “nucleus” and an “electron”.

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