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.

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 Quantum backflow in solutions to the Dirac equation of the spin-1 2 free particle

2018 ◽  
Vol 33 (32) ◽  
pp. 1850186 ◽  
Author(s):  
Hong-Yi Su ◽  
Jing-Ling Chen
Keyword(s):  
Quantum Mechanics ◽  
Dirac Equation ◽  
Relativistic Particle ◽  
Relativistic Quantum ◽  
Free Particle ◽  
Negative Energy ◽  
Dirac Particle ◽  
Relativistic Quantum Mechanics ◽  
Probability Current ◽  
Negative Probability

It was known that a free, non-relativistic particle in a superposition of positive momenta can, in certain cases, bear a negative probability current — hence termed quantum backflow. Here, it is shown that more variations can be brought about for a free Dirac particle, particularly when negative-energy solutions are taken into account. Since any Dirac particle can be understood as an antiparticle that acts oppositely (and vice versa), quantum backflow is found to arise in the superposition (i) of a well-defined momentum but different signs of energies, or more remarkably (ii) of different signs of both momenta and energies. Neither of these cases has a counterpart in non-relativistic quantum mechanics. A generalization by using the field-theoretic formalism is also presented and discussed.

scholarly journals An extended Dirac equation in noncommutative spacetime

2016 ◽  
Vol 31 (15) ◽  
pp. 1650089 ◽  
Author(s):  
R. Vilela Mendes
Keyword(s):  
Quantum Mechanics ◽  
Dirac Equation ◽  
Relativistic Quantum ◽  
Large Mass ◽  
Exterior Algebra ◽  
Relativistic Quantum Mechanics ◽  
Spacetime Geometry ◽  
Noncommutative Spacetime ◽  
Extended Dirac Equation

Stabilizing, by deformation, the algebra of relativistic quantum mechanics a noncommutative spacetime geometry is obtained. The exterior algebra of this geometry leads to an extended massless Dirac equation which has both a massless and a large mass solution. The nature of the solutions is discussed as well as the effects of coupling the two solutions.

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 THE LIENARD–WIECHERT POTENTIAL OF CHARGED SCALAR PARTICLES AND THEIR RELATION TO SCALAR ELECTRODYNAMICS IN THE REST-FRAME INSTANT FORM

1998 ◽  
Vol 13 (16) ◽  
pp. 2791-2831 ◽  
Author(s):  
DAVID ALBA ◽  
LUCA LUSANNA
Keyword(s):  
Electromagnetic Field ◽  
Dirac Equation ◽  
Rest Frame ◽  
Coulomb Gauge ◽  
Charged Scalar ◽  
Scalar Particles ◽  
Field System ◽  
Instant Form ◽  
Hamilton Equations ◽  
New Type

After a summary of a recently proposed new type of instant form of dynamics (the Wigner-covariant rest-frame instant form), the reduced Hamilton equations in the covariant rest-frame Coulomb gauge for the isolated system of N scalar particles with pseudoclassical Grassmann-valued electric charges plus the electromagnetic field are studied. The Lienard–Wiechert potentials of the particles are evaluated and it is shown how the causality problems of the Abraham–Lorentz–Dirac equation are solved at the pseudoclassical level. Then, the covariant rest-frame description of scalar electrodynamics is given. Applying to it the Feshbach–Villars formalism, the connection with the particle plus electromagnetic field system is found.

The Dirac Equation

2007 ◽  
Author(s):  
Kenneth G. Dyall ◽  
Knut Faegri
Keyword(s):  
Quantum Mechanics ◽  
Dirac Equation ◽  
Relativistic Quantum ◽  
Type Equation ◽  
Nonrelativistic Limit ◽  
Relativistic Quantum Mechanics ◽  
Electronic Systems ◽  
Nonrelativistic Case ◽  
Relativistic Description ◽  
Basic Features

The purpose of this chapter is to introduce the Dirac equation, which will provide us with a basis for developing the relativistic quantum mechanics of electronic systems. Thus far we have reviewed some basic features of the classical relativistic theory, which is the foundation of relativistic quantum theory. As in the nonrelativistic case, quantum mechanical equations may be obtained from the classical relativistic particle equations by use of the correspondence principle, where we replace classical variables by operators. Of particular interest are the substitutions In terms of the momentum four-vector introduced earlier, this yields In going from a classical relativistic description to relativistic quantum mechanics, we require that the equations obtained are invariant under Lorentz transformations. Other basic requirements, such as gauge invariance, must also apply to the equations of relativistic quantum mechanics. We start this chapter by reexamining the quantization of the nonrelativistic Hamiltonian and draw out some features that will be useful in the quantization of the relativistic Hamiltonian. We then turn to the Dirac equation and sketch its derivation. We discuss some properties of the equation and its solutions, and show how going to the nonrelativistic limit reduces it to a Schrödinger-type equation containing spin.

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