scholarly journals REMARKS ON THE SPHERICAL WAVES OF THE DIRAC FIELD ON de SITTER SPACETIME

2006 ◽  
Vol 21 (16) ◽  
pp. 1313-1318 ◽  
Author(s):  
ION I. COTĂESCU ◽  
RADU RACOCEANU ◽  
COSMIN CRUCEAN
Keyword(s):  
Dirac Equation ◽  
Dirac Field ◽  
De Sitter Spacetime ◽  
Moving Frames ◽  
De Sitter ◽  
Spherical Waves ◽  
Commuting Operators ◽  
Quantum Numbers ◽  
Sitter Spacetime

The Shishkin's solutions of the Dirac equation in spherical moving frames of the de Sitter spacetime are investigated pointing out the set of commuting operators whose eigenvalues determine the integration constants. It is shown that these depend on the usual angular quantum numbers and, in addition, on the value of the scalar momentum. With these elements a new result is obtained finding the system of solutions normalized (in generalized sense) in the scale of scalar momentum.

scholarly journals COULOMB SCATTERING OF THE DIRAC FERMIONS ON DE SITTER EXPANDING UNIVERSE

2007 ◽  
Vol 22 (34) ◽  
pp. 2573-2585 ◽  
Author(s):  
COSMIN CRUCEAN
Keyword(s):  
Dirac Equation ◽  
Exact Solutions ◽  
Cross Section ◽  
Dirac Field ◽  
Coulomb Scattering ◽  
De Sitter Spacetime ◽  
Dirac Fermions ◽  
Final States ◽  
De Sitter ◽  
Sitter Spacetime

The lowest order contribution of the amplitude of the Dirac–Coulomb scattering in de Sitter spacetime 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 spacetime with a given momentum and helicity. One studies the difficulties that arises when one passes from the amplitude to cross section.

scholarly journals Emergent $$\alpha $$-like fermionic vacuum structure and entanglement in the hyperbolic de Sitter spacetime

2019 ◽  
Vol 79 (9) ◽  
Author(s):  
Sourav Bhattacharya ◽  
Shankhadeep Chakrabortty ◽  
Shivang Goyal
Keyword(s):  
Quantum Correlations ◽  
Dirac Field ◽  
De Sitter Spacetime ◽  
De Sitter ◽  
Local Modes ◽  
Vacuum Structure ◽  
Continuous Parameter ◽  
Sitter Spacetime ◽  
Global Modes ◽  
De Sitter Vacua

Abstract We report a non-trivial feature of the vacuum structure of free massive or massless Dirac fields in the hyperbolic de Sitter spacetime. Here we have two causally disconnected regions, say R and L separated by another region, C. We are interested in the field theory in $$R\cup L$$R∪L to understand the long range quantum correlations between R and L. There are local modes of the Dirac field having supports individually either in R or L, as well as global modes found via analytically continuing the R modes to L and vice versa. However, we show that unlike the case of a scalar field, the analytic continuation does not preserve the orthogonality of the resulting global modes. Accordingly, we need to orthonormalise them following the Gram–Schmidt prescription, prior to the field quantisation in order to preserve the canonical anti-commutation relations. We observe that this prescription naturally incorporates a spacetime independent continuous parameter, $$\theta _{\mathrm{RL}}$$θRL, into the picture. Thus interestingly, we obtain a naturally emerging one-parameter family of $$\alpha $$α-like de Sitter vacua. The values of $$\theta _{\mathrm{RL}}$$θRL yielding the usual thermal spectra of massless created particles are pointed out. Next, using these vacua, we investigate both entanglement and Rényi entropies of either of the regions and demonstrate their dependence on $$\theta _{\mathrm{RL}}$$θRL.

De Sitter spacetime as a momentum measuring apparatus

Open Physics ◽  
2012 ◽  
Vol 10 (1) ◽  
Author(s):  
Nistor Nicolaevici
Keyword(s):  
Dirac Equation ◽  
De Sitter Spacetime ◽  
Measuring Apparatus ◽  
De Sitter ◽  
Measuring Process ◽  
Wave Solutions ◽  
Sitter Spacetime ◽  
Classical Trajectories ◽  
Quantum Wave ◽  
Different Parts

AbstractWe discuss the evolution of a quantum wave packet in the expanding de Sitter spacetime using the plane wave solutions of the Dirac equation. We concentrate on the case of large negative times when the packet approaches the event horizon and confirm that the evolution accords with that expected from the classical trajectories. We point out that in certain conditions the packet can split into two components that become localized at different parts of the horizon and that this effect can be seen, in an idealized sense, as a measuring process for the momentum of the particle, in direct analogy with the measurement of spin in a Stern-Gerlach experiment.

scholarly journals Time evolution of the free Dirac field in spatially flat FLRW space–times

2020 ◽  
Vol 35 (32) ◽  
pp. 2030019
Author(s):  
Ion I. Cotăescu
Keyword(s):  
Dirac Equation ◽  
Rest Frame ◽  
Relativistic Quantum ◽  
Fundamental Solutions ◽  
Relativistic Quantum Mechanics ◽  
Dirac Field ◽  
De Sitter ◽  
Spherical Waves ◽  
New Type ◽  
First Time

The framework of the relativistic quantum mechanics on spatially flat FLRW space–times is considered for deriving the analytical solutions of the Dirac equation in different local charts of these manifolds. Systems of commuting conserved operators are used for determining the fundamental solutions as common eigenspinors giving thus physical meaning to the integration constants related to the eigenvalues of these operators. Since these systems, in general, are incomplete on the FLRW space–times there are integration constants that must be fixed by setting the vacuum either as the traditional adiabatic one or as the rest frame vacuum we proposed recently. All the known solutions of the Dirac equation on these manifolds are discussed in all details and a new type of spherical waves of given energy in the de Sitter expanding universe is reported here for the first time.

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