Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userOn the $kappa$-Dirac Oscillator revisited
146
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
This Letter is based on the $kappa$-Dirac equation, derived from the $kappa$-Poincar{e}-Hopf algebra. It is shown that the $kappa$-Dirac equation preserves parity while breaks charge conjugation and time reversal symmetries. Introducing the Dirac oscillator prescription, $mathbf{p}tomathbf{p}-imomegabetamathbf{r}$, in the $kappa$-Dirac equation, one obtains the $kappa$-Dirac oscillator. Using a decomposition in terms of spin angular functions, one achieves the deformed radial equations, with the associated deformed energy eigenvalues and eigenfunctions. The deformation parameter breaks the infinite degeneracy of the Dirac oscillator. In the case where $varepsilon=0$, one recovers the energy eigenvalues and eigenfunctions of the Dirac oscillator.
rate research
Read More
We obtain exact solutions of the (2+1) dimensional Dirac oscillator in a homogeneous magnetic field within the Anti-Snyder modified uncertainty relation characterized by a momentum cut-off ($pleq p_{text{max}}=1/ sqrt{beta}$). In ordinary quantum mechanics ($betato 0$) this system is known to have a single left-right chiral quantum phase transition (QPT). We show that a finite momentum cut-off modifies the spectrum introducing additional quantum phase transitions. It is also shown that the presence of momentum cut-off modifies the degeneracy of the states.
We return to the description of the damped harmonic oscillator by means of a closed quantum theory with a general assessment of previous works, in particular the Bateman-Caldirola-Kanai model and a new model recently proposed by one of the authors. We show the local equivalence between the two models and argue that latter has better high energy behavior and is naturally connected to existing open-quantum-systems approaches.
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.
We present a new construction for the Hodge operator for differential manifolds based on a Fourier (Berezin)-integral representation. We find a simple formula for the Hodge dual of the wedge product of differential forms, using the (Berezin)-convolution. The present analysis is easily extended to supergeometry and to non-commutative geometry.
We revisit the Virasoro constraints and explore the relation to the Hirota bilinear equations. We furthermore investigate and provide the solution to non-homogeneous Virasoro constraints, namely those coming from matrix models whose domain of integration has boundaries. In particular, we provide the example of Hermitean matrices with positive eigenvalues in which case one can find a solution by induction on the rank of the matrix model.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
