scholarly journals NEW DIRAC QUANTUM MODES IN MOVING FRAMES OF THE DE SITTER SPACE–TIME

2008 ◽  
Vol 23 (22) ◽  
pp. 3707-3720 ◽  
Author(s):  
ION I. COTĂESCU ◽  
COSMIN CRUCEAN
Keyword(s):  
Quantum Mechanics ◽  
Dirac Equation ◽  
Complete System ◽  
Plane Waves ◽  
De Sitter Space ◽  
Space Time ◽  
Principal Result ◽  
Moving Frames ◽  
De Sitter ◽  
Schrödinger Picture

Recently a new time-evolution picture of the Dirac quantum mechanics was defined in charts with spatially flat Robertson–Walker metrics, under the name of Schrödinger picture (I. I. Cotăescu, Mod. Phys. Lett. A22, 2965 (2007)). In the present paper, new Dirac quantum modes are found in moving charts of the de Sitter space–time using the technical advantages offered by this picture. The principal result is a new set of energy eigenspinors which behave as polarized plane waves and form a complete system of orthonormalized solutions of the free Dirac equation.

Propagation of Gamma packets on de Sitter space–time

2017 ◽  
Vol 32 (27) ◽  
pp. 1750167
Author(s):  
Alin-Nicolae Chilom
Keyword(s):  
Quantum Mechanics ◽  
Uncertainty Relation ◽  
De Sitter Space ◽  
Space Time ◽  
De Sitter ◽  
Scalar Quantum ◽  
Energy And Momentum

The (1[Formula: see text]+[Formula: see text]1) scalar quantum mechanics on the de Sitter space–time is outlined focusing on the momentum-energy statistics and the propagation of the packets that minimize the uncertainty relation between energy and momentum.

scholarly journals REDUCTION FORMALISM FOR DIRAC FERMIONS ON DE SITTER SPACE–TIME

2008 ◽  
Vol 23 (07) ◽  
pp. 1075-1087 ◽  
Author(s):  
COSMIN CRUCEAN ◽  
RADU RACOCEANU
Keyword(s):  
Perturbation Theory ◽  
Dirac Equation ◽  
Exact Solutions ◽  
Scattering Amplitude ◽  
De Sitter Space ◽  
Space Time ◽  
Green Functions ◽  
Dirac Fermions ◽  
De Sitter

The reduction formulas for Dirac fermions is derived using the exact solutions of free Dirac equation on de Sitter space–time. In the framework of the perturbation theory one studies the Green functions and derives the scattering amplitude in the first orders of perturbation theory.

scholarly journals DIRAC–COULOMB SCATTERING WITH PLANE WAVE ENERGY EIGENSPINORS ON DE SITTER EXPANDING UNIVERSE

2008 ◽  
Vol 23 (09) ◽  
pp. 1351-1359 ◽  
Author(s):  
ION I. COTĂESCU ◽  
COSMIN CRUCEAN
Keyword(s):  
Dirac Equation ◽  
Plane Wave ◽  
Wave Energy ◽  
De Sitter Space ◽  
Space Time ◽  
Dirac Field ◽  
Coulomb Scattering ◽  
Final States ◽  
De Sitter ◽  
Scattering Process

The lowest order contribution of the amplitude of Dirac–Coulomb scattering in de Sitter space–time is calculated assuming that the initial and final states of the Dirac field are described by exact solutions of the free Dirac equation on de Sitter space–time with a given energy and helicity. We find that the total energy is conserved in the scattering process.

scholarly journals TWO-POINT FUNCTIONS AND QUANTUM FIELDS IN DE SITTER UNIVERSE

1996 ◽  
Vol 08 (03) ◽  
pp. 327-391 ◽  
Author(s):  
JACQUES BROS ◽  
UGO MOSCHELLA
Keyword(s):  
Plane Waves ◽  
Thermal Characterization ◽  
De Sitter Space ◽  
Space Time ◽  
Space Structure ◽  
Spectral Condition ◽  
De Sitter ◽  
Type Representation ◽  
Tube Domains ◽  
De Sitter Universe

We present a theory of general two-point functions and of generalized free fields in d-dimensional de Sitter space-time which closely parallels the corresponding Minkowskian theory. The usual spectral condition is now replaced by a certain geodesic spectral condition, equivalent to a precise thermal characterization of the corresponding “vacuum” states. Our method is based on the geometry of the complex de Sitter space-time and on the introduction of a class of holomorphic functions on this manifold, called perikernels, which reproduce mutatis mutandis the structural properties of the two-point correlation functions of the Minkowskian quantum field theory. The theory contains as basic elementary case the linear massive field models in their “preferred” representation. The latter are described by the introduction of de Sitter plane waves in their tube domains which lead to a new integral representation of the two-point functions and to a Fourier-Laplace type transformation on the hyperboloid. The Hilbert space structure of these theories is then analysed by using this transformation. In particular we show the Reeh-Schlieder property. For general two-point functions, a substitute to the Wick rotation is defined both in complex space-time and in the complex mass variable, and substantial results concerning the derivation of Källen-Lehmann type representation are obtained.

scholarly journals THE SCHRÖDINGER PICTURE OF THE DIRAC QUANTUM MECHANICS ON SPATIALLY FLAT ROBERTSON–WALKER BACKGROUNDS

2007 ◽  
Vol 22 (39) ◽  
pp. 2965-2969 ◽  
Author(s):  
ION I. COTĂESCU
Keyword(s):  
Quantum Mechanics ◽  
Gravitational Field ◽  
Dirac Equation ◽  
Time Evolution ◽  
Hamiltonian Operator ◽  
De Sitter ◽  
Minimal Coupling ◽  
Cartesian Coordinates ◽  
Schrödinger Picture

The time evolution Schrödinger picture of the Dirac quantum mechanics is defined in charts with spatially flat Robertson–Walker metrics and Cartesian coordinates. The main observables of this picture are identified, including the interacting part of the Hamiltonian operator produced by the minimal coupling with the gravitational field. It is shown that in this approach new Dirac quantum modes on de Sitter spacetimes may be found analytically solving the Dirac equation.

Noncommutative scalar field in de Sitter space–time and pair creation process

2021 ◽  
Vol 36 (02) ◽  
pp. 2150011
Author(s):  
Nabil Mehdaoui ◽  
Lamine Khodja ◽  
Salah Haouat
Keyword(s):  
Scalar Field ◽  
Chemical Potential ◽  
De Sitter Space ◽  
Space Time ◽  
Pair Creation ◽  
De Sitter ◽  
Creation Process ◽  
Scalar Particles ◽  
Constant Electromagnetic Field

In this work, we address the process of pair creation of scalar particles in [Formula: see text] de Sitter space–time in presence of a constant electromagnetic field by applying the noncommutativity on the scalar field up to first-order in [Formula: see text]. We calculate the density of particles created in the vacuum by the mean of the Bogoliubov transformations. In contrast to a previous result, we show that noncommutativity contributes to the pair creation process. We find that the noncommutativity plays the same role of chemical potential and gives an important interest for studies at high energies.

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