scholarly journals EFFECTS OF A MIXED VECTOR-SCALAR KINK-LIKE POTENTIAL FOR SPINLESS PARTICLES IN TWO-DIMENSIONAL SPACE–TIME

2007 ◽  
Vol 22 (14n15) ◽  
pp. 2609-2618 ◽  
Author(s):  
ANTONIO S. DE CASTRO
Keyword(s):  
Morse Potential ◽  
Dimensional Space ◽  
Liouville Problem ◽  
Bounded Solutions ◽  
Compton Wavelength ◽  
Apparent Paradox ◽  
Exactly Solvable ◽  
Relativistic Problem ◽  
Dimensional Space Time ◽  
Sturm Liouville

The intrinsically relativistic problem of spinless particles subject to a general mixing of vector and scalar kink-like potentials (~ tanh γx) is investigated. The problem is mapped into the exactly solvable Sturm–Liouville problem with the Rosen–Morse potential and exact bounded solutions for particles and antiparticles are found. The behavior of the spectrum is discussed in some detail. An apparent paradox concerning the uncertainty principle is solved by recurring to the concept of effective Compton wavelength.

scholarly journals FORMULATION OF THE SPINOR FIELD IN THE PRESENCE OF A MINIMAL LENGTH BASED ON THE QUESNE–TKACHUK ALGEBRA

2011 ◽  
Vol 26 (29) ◽  
pp. 4981-4990 ◽  
Author(s):  
S. K. MOAYEDI ◽  
M. R. SETARE ◽  
H. MOAYERI ◽  
M. POORAKBAR
Keyword(s):  
Spinor Field ◽  
Dimensional Space ◽  
Minimal Length ◽  
Compton Wavelength ◽  
First Order ◽  
Deformed Algebra ◽  
Dimensional Space Time ◽  
Higher Order Derivative ◽  
Modified Dirac Equation ◽  
Two Parameter

In 2006 Quesne and Tkachuk (J. Phys. A: Math. Gen.39, 10909, (2006)) introduced a (D+1)-dimensional (β, β′)-two-parameter Lorentz-covariant deformed algebra which leads to a nonzero minimal length. In this work, the Lagrangian formulation of the spinor field in a (3+1)-dimensional space–time described by Quesne–Tkachuk Lorentz-covariant deformed algebra is studied in the case where β′ = 2β up to first order over deformation parameter β. It is shown that the modified Dirac equation which contains higher order derivative of the wave function describes two massive particles with different masses. We show that physically acceptable mass states can only exist for [Formula: see text]. Applying the condition [Formula: see text] to an electron, the upper bound for the isotropic minimal length becomes about 3 ×10-13 m. This value is near to the reduced Compton wavelength of the electron [Formula: see text] and is not incompatible with the results obtained for the minimal length in previous investigations.

Sturm-Liouville Problem for Stationary Differential Operator with Nonlocal Two-Point Boundary Conditions

2006 ◽  
Vol 11 (1) ◽  
pp. 47-78 ◽  
Author(s):  
S. Pečiulytė ◽  
A. Štikonas
Keyword(s):  
Boundary Condition ◽  
Differential Operator ◽  
Boundary Conditions ◽  
Nonlocal Boundary Condition ◽  
Nonlocal Boundary ◽  
Liouville Problem ◽  
Complex Case ◽  
Qualitative Behavior ◽  
Point Boundary ◽  
Sturm Liouville

The Sturm-Liouville problem with various types of two-point boundary conditions is considered in this paper. In the first part of the paper, we investigate the Sturm-Liouville problem in three cases of nonlocal two-point boundary conditions. We prove general properties of the eigenfunctions and eigenvalues for such a problem in the complex case. In the second part, we investigate the case of real eigenvalues. It is analyzed how the spectrum of these problems depends on the boundary condition parameters. Qualitative behavior of all eigenvalues subject to the nonlocal boundary condition parameters is described.

Topology knots and hierarchy problem

2019 ◽  
Author(s):  
Vitaly Kuyukov
Keyword(s):  
Quantum Theory ◽  
String Theory ◽  
Quantum Gravity ◽  
Dimensional Space ◽  
Space Time ◽  
Elementary Particles ◽  
Hierarchy Problem ◽  
Topological Quantum ◽  
Dimensional Space Time ◽  
New Formula

Many approaches to quantum gravity consider the revision of the space-time geometry and the structure of elementary particles. One of the main candidates is string theory. It is possible that this theory will be able to describe the problem of hierarchy, provided that there is an appropriate Calabi-Yau geometry. In this paper we will proceed from the traditional view on the structure of elementary particles in the usual four-dimensional space-time. The only condition is that quarks and leptons should have a common emerging structure. When a new formula for the mass of the hierarchy is obtained, this structure arises from topological quantum theory and a suitable choice of dimensional units.

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