Self-consistency in Theories with a Minimal Length

The aim of this paper is to clarify the relation between three different approaches of theories with a minimal length scale: A modification of the Lorentz-group in the 'Deformed Special Relativity', theories with a 'Generalized Uncertainty Principle' and those with 'Modified Dispersion Relations'. It is shown that the first two are equivalent, how they can be translated into each other, and how the third can be obtained from them. An adequate theory with a minimal length scale requires all three features to be present.Comment: typos corrected, published with new title following referee's advic

Bohr-Sommerfeld quantization and meson spectroscopy

We use the Bohr-Sommerfeld quantization approach in the context of constituent quark models. This method provides, for the Cornell potential, analytical formulae for the energy spectra which closely approximate numerical exact calculations performed with the Schrodinger or the spinless Salpeter equations. The Bohr-Sommerfeld quantization procedure can also be used to calculate other observables such as r.m.s. radius or wave function at the origin. Asymptotic dependence of these observables on quantum numbers are also obtained in the case of potentials which behave asymptotically as a power-law. We discuss the constraints imposed by these formulae on the dynamics of the quark-antiquark interaction.Comment: 13 page

Baryon spectra with instanton induced forces

Except the vibrational excitations of $K$ and $K^*$ mesons, the main features of spectra of mesons composed of quarks $u$, $d$, and $s$ can be quite well described by a semirelativistic potential model including instanton induced forces. The spectra of baryons composed of the same quarks is studied using the same model. The results and the limitations of this approach are described. Some possible improvements are suggested.Comment: 5 figure

Effect of Minimal lengths on Electron Magnetism

We study the magnetic properties of electron in a constant magnetic field and confined by a isotropic two dimensional harmonic oscillator on a space where the coordinates and momenta operators obey generalized commutation relations leading to the appearance of a minimal length. Using the momentum space representation we determine exactly the energy eigenvalues and eigenfunctions. We prove that the usual degeneracy of Landau levels is removed by the presence of the minimal length in the limits of weak and strong magnetic field.The thermodynamical properties of the system, at high temperature, are also investigated showing a new magnetic behavior in terms of the minimal length.Comment: 14 pages, 1 figur

A unified meson-baryon potential

We study the spectra of mesons and baryons, composed of light quarks, in the framework of a semirelativistic potential model including instanton induced forces. We show how a simple modification of the instanton interaction in the baryon sector allows a good description of the meson and the baryon spectra using an interaction characterized by a unique set of parameters.Comment: 7 figure

Quantum Gravitational Corrections to the Real Klein-Gordon Field in the Presence of a Minimal Length

The (D+1)-dimensional $(\beta,\beta')$-two-parameter Lorentz-covariant deformed algebra introduced by Quesne and Tkachuk [C. Quesne and V. M. Tkachuk, J. Phys. A: Math. Gen. \textbf {39}, 10909 (2006).], leads to a nonzero minimal uncertainty in position (minimal length). The Klein-Gordon equation in a (3+1)-dimensional space-time described by Quesne-Tkachuk Lorentz-covariant deformed algebra is studied in the case where $\beta'=2\beta$ up to first order over deformation parameter $\beta$. It is shown that the modified Klein-Gordon equation which contains fourth-order derivative of the wave function describes two massive particles with different masses. We have shown that physically acceptable mass states can only exist for $\beta<\frac{1}{8m^{2}c^{2}}$ which leads to an isotropic minimal length in the interval $10^{-17}m<(\bigtriangleup X^{i})_{0}<10^{-15}m$. Finally, we have shown that the above estimation of minimal length is in good agreement with the results obtained in previous investigations.Comment: 10 pages, no figur

Some Aspects of Minimal Length Quantum Mechanics

String theory, quantum geometry, loop quantum gravity and black hole physics all indicate the existence of a minimal observable length on the order of Planck length. This feature leads to a modification of Heisenberg uncertainty principle. Such a modified Heisenberg uncertainty principle is referred as gravitational uncertainty principle(GUP) in literatures. This proposal has some novel implications on various domains of theoretical physics. Here, we study some consequences of GUP in the spirit of Quantum mechanics. We consider two problem: a particle in an one-dimensional box and momentum space wave function for a "free particle". In each case we will solve corresponding perturbational equations and compare the results with ordinary solutions.Comment: 9 pages, one eps figur