We study the relativistic quantum dynamics of a DKP oscillator field subject to a linear interaction in cosmic string space-time in order to better understand the effects of gravitational fields produced by topological defects on the scalar field. We obtain the solution of DKP oscillator in the cosmic string background. Also, we solve it with an ansatz in presence of linear interaction. We obtain the eigenfunctions and the energy levels of the relativistic field in that background.
We examine the non-inertial effects of a rotating frame on a Dirac oscillator in a cosmic string space-time with non-commutative geometry in phase space. We observe that the approximate bound-state solutions are related to the biconfluent Heun polynomials. The related energies cannot be obtained in a closed form for all the bound states. We find the energy of the fundamental state analytically by taking into account the hard-wall confining condition. We describe how the ground-state energy scales with the new non-commutative term as well as with the other physical parameters of the system.
We study the SL(2,R) WZWN string model describing bosonic string theory in AdS_3 space-time as a deformed oscillator together with its mass spectrum and the string modified SL(2,R) uncertainty relation. The SL(2,R) string oscillator is far more quantum (with higher quantum uncertainty) and more excited than the non deformed one. This is accompassed by the highly excited string mass spectrum which is drastically changed with respect to the low excited one. The highly excited quantum string regime and the low excited semiclassical regime of the SL(2,R) string model are described and shown to be the quantum-classical dual of each other in the precise sense of the usual classical-quantum duality. This classical-quantum realization is not assumed nor conjectured. The quantum regime (high curvature) displays a modified Heisenbergs uncertainty relation, while the classical (low curvature) regime has the usual quantum mechanics uncertainty principle.
The Dirac equation with both scalar and vector couplings describing the dynamics of a two-dimensional Dirac oscillator in the cosmic string spacetime is considered. We derive the Dirac-Pauli equation and solve it in the limit of the spin and the pseudo-spin symmetries. We analyze the presence of cylindrical symmetric scalar potentials which allows us to provide analytic solutions for the resultant field equation. By using an appropriate ansatz, we find that the radial equation is a biconfluent Heun-like differential equation. The solution of this equation provides us with more than one expression for the energy eigenvalues of the oscillator. We investigate these energies and find that there is a quantum condition between them. We study this condition in detail and find that it requires the fixation of one of the physical parameters involved in the problem. Expressions for the energy of the oscillator are obtained for some values of the quantum number $n$. Some particular cases which lead to known physical systems are also addressed.
String theory developed by demanding consistency with quantum mechanics. In this paper we wish to reverse the reasoning. We pretend open string field theory is a fully consistent definition of the theory - it is at least a self consistent sector. Then we find in its structure that the rules of quantum mechanics emerge from the non-commutative nature of the basic string joining/splitting interactions, thus deriving rather than assuming the quantum commutation rules among the usual canonical quantum variables for all physical systems derivable from open string field theory. Morally we would apply such an argument to M-theory to cover all physics. If string or M-theory really underlies all physics, it seems that the door has been opened to an understanding of the origins of quantum mechanics.
In this paper the relativistic quantum dynamics of a spin-1/2 neutral particle with a magnetic moment $mu$ in the cosmic string spacetime is reexamined by applying the von Neumann theory of self--adjoint extensions. Contrary to previous studies where the interaction between the spin and the line of charge is neglected, here we consider its effects. This interaction gives rise to a point interaction: $boldsymbol{ abla} cdot mathbf{E}= (2lambda/alpha)delta(r)/r$. Due to the presence of the Dirac delta function, by applying an appropriated boundary condition provided by the theory of self--adjoint extensions, irregular solutions for the Hamiltonian are allowed. We address the scattering problem obtaining the phase shift, S-matrix and the scattering amplitude. The scattering amplitude obtained shows a dependency with energy which stems from the fact that the helicity is not conserved in this system. Examining the poles of the S-matrix we obtain an expression for the bound states. The presence of bound states for this system has not been discussed before in the literature.
Mansoureh Hosseinpour
,Hassan Hassanabadi
,Fabiano M. Andrade
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(2017)
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"The DKP oscillator with a linear interaction in the cosmic string space-time"
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Fabiano Andrade
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