In the present paper we investigate the deformed problem of the Dirac electrons in the non-commut... more In the present paper we investigate the deformed problem of the Dirac electrons in the non-commutative geometry and in the Lie-admissible formulation of the quantum gravity. The time and momentum deformations are introduced through the Caldirola-Montaldi (C.M.) model as well as the Small-Distance-Derivative (S.D.D.) model. The above models are special cases of the Lie-admissible theory. The results are based on the theory developed by Gonzalez-Diaz who used the (S.D.D.) model to construct a modified Lie-admissible Wheeler-De Witt equation. The interpretation of this equation is that the universe has a non zero total energy where values coincide with the corresponding values of a harmonic oscillator with Planck mass M * . It is an open system which interacts with some sort of “exterior” world and it is created by a kind of physical reality. Also the group velocity, after applying the two models, to the Dirac theory, leads to a velocity greater of c and satisfies the Santilli’s hypoth...
In the present paper, we study a two-dimensional harmonic oscillator in a constant magnetic field... more In the present paper, we study a two-dimensional harmonic oscillator in a constant magnetic field in noncommuting space. We use the following Hamiltonian [Formula: see text] with commutation relations [Formula: see text] and [Formula: see text]. The parameter λ expresses the presence of the magnetic field. We find the exact propagator of the system and the time evolution of the basic operators. We prove that the system is equivalent to a two-dimensional system where the operators of momentum and coordinates of the second dimension satisfy a deformed commutation relation [Formula: see text]. The deformation parameter, μ, depends on λ and θ, and is independent of the Hamiltonian. Finally, we investigate the thermodynamic properties of the system in Boltzmann statistics. We find the statistical density matrix and the partition function, which is equivalent to that of a two-dimensional harmonic oscillator with two deformed frequencies Ω1 and Ω2.
International Journal of Modern Physics B - IJMPB, 2006
In the present paper we study the deformed harmonic oscillator for the non-Hermitian operator H=(... more In the present paper we study the deformed harmonic oscillator for the non-Hermitian operator H=(alpha )/(2m) (hat{p}1+ (lambda)/(hbar )hat q2;)2+ (beta momega 2)/(2)(hat q1-(theta )/(2 hbar ) hat p2; )2 where lambda,theta are real positive parameters, since the parameters alpha,beta,m are for the general case complex. For the case alpha=1,beta=1 and mass m real, we find the eigenfunctions and eigenvalues of energy, the coherent states, the time evolution of the operators \hat{q}_i, \hat{p}_j$ in the Heisenberg picture and the uncertainty relations. In this case the operator ℋ is Hermitian and PT-symmetric. Also for the case m complex alpha=1,beta=1, the operator ℋ is non-Hermitian and no more PT symmetric, but CPT symmetric with real discrete positive spectrum and the CPT symmetry is preserved. In the general case alpha,beta,m complex, for the non-Hermitian operator ℋ, we obtain complex spectrum and for the special values of the complex parameters alpha,beta the spectrum is real di...
In the present paper we investigate the deformed problem of the Dirac electrons in the non-commut... more In the present paper we investigate the deformed problem of the Dirac electrons in the non-commutative geometry and in the Lie-admissible formulation of the quantum gravity. The time and momentum deformations are introduced through the Caldirola-Montaldi (C.M.) model as well as the Small-Distance-Derivative (S.D.D.) model. The above models are special cases of the Lie-admissible theory. The results are based on the theory developed by Gonzalez-Diaz who used the (S.D.D.) model to construct a modified Lie-admissible Wheeler-De Witt equation. The interpretation of this equation is that the universe has a non zero total energy where values coincide with the corresponding values of a harmonic oscillator with Planck mass M * . It is an open system which interacts with some sort of “exterior” world and it is created by a kind of physical reality. Also the group velocity, after applying the two models, to the Dirac theory, leads to a velocity greater of c and satisfies the Santilli’s hypoth...
In the present paper, we study a two-dimensional harmonic oscillator in a constant magnetic field... more In the present paper, we study a two-dimensional harmonic oscillator in a constant magnetic field in noncommuting space. We use the following Hamiltonian [Formula: see text] with commutation relations [Formula: see text] and [Formula: see text]. The parameter λ expresses the presence of the magnetic field. We find the exact propagator of the system and the time evolution of the basic operators. We prove that the system is equivalent to a two-dimensional system where the operators of momentum and coordinates of the second dimension satisfy a deformed commutation relation [Formula: see text]. The deformation parameter, μ, depends on λ and θ, and is independent of the Hamiltonian. Finally, we investigate the thermodynamic properties of the system in Boltzmann statistics. We find the statistical density matrix and the partition function, which is equivalent to that of a two-dimensional harmonic oscillator with two deformed frequencies Ω1 and Ω2.
International Journal of Modern Physics B - IJMPB, 2006
In the present paper we study the deformed harmonic oscillator for the non-Hermitian operator H=(... more In the present paper we study the deformed harmonic oscillator for the non-Hermitian operator H=(alpha )/(2m) (hat{p}1+ (lambda)/(hbar )hat q2;)2+ (beta momega 2)/(2)(hat q1-(theta )/(2 hbar ) hat p2; )2 where lambda,theta are real positive parameters, since the parameters alpha,beta,m are for the general case complex. For the case alpha=1,beta=1 and mass m real, we find the eigenfunctions and eigenvalues of energy, the coherent states, the time evolution of the operators \hat{q}_i, \hat{p}_j$ in the Heisenberg picture and the uncertainty relations. In this case the operator ℋ is Hermitian and PT-symmetric. Also for the case m complex alpha=1,beta=1, the operator ℋ is non-Hermitian and no more PT symmetric, but CPT symmetric with real discrete positive spectrum and the CPT symmetry is preserved. In the general case alpha,beta,m complex, for the non-Hermitian operator ℋ, we obtain complex spectrum and for the special values of the complex parameters alpha,beta the spectrum is real di...
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Papers by Antony Streklas