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 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.

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.

A time operator in the simulations of the Dirac equation

2019 ◽  
Vol 34 (22) ◽  
pp. 1950114 ◽  
Author(s):  
M. Bauer
Keyword(s):  
Quantum Mechanics ◽  
Dirac Equation ◽  
Relativistic Quantum ◽  
Einstein Condensate ◽  
Time Operator ◽  
Relativistic Quantum Mechanics ◽  
Electron Motion ◽  
Klein Paradox ◽  
Bose Einstein Condensate ◽  
Bose Einstein

Simulations of the Dirac equation have allowed to mimic measurably the predicted unusual characteristics of the electron motion, e.g. Zitterbewegung and Klein paradox that are beyond current technical capabilities. In this paper, it is shown that a Bose–Einstein condensate experiment carried out corroborates these results, but in addition exhibits a particular feature of an observable represented by a Dirac self-adjoint time operator introduced in relativistic quantum mechanics.

Towards a Relativistic Quantum Mechanics

2017 ◽  
Author(s):  
Laurent Baulieu ◽  
John Iliopoulos ◽  
Roland Sénéor
Keyword(s):  
Quantum Mechanics ◽  
Dirac Equation ◽  
Degrees Of Freedom ◽  
Relativistic Quantum ◽  
Negative Energy ◽  
Relativistic Quantum Mechanics ◽  
Relativistic Limit ◽  
Probability Current ◽  
Klein Gordon ◽  
Relativistic Equations

Towards a relativistic quantum mechanics. Klein–Gordon and the problems of the probability current and the negative energy solutions. The Dirac equation and negative energies. P, C, and T symmetries. Positrons. The Schrödinger equation as the non-relativistic limit of relativistic equations. Majorana and Weyl equations. Relativistic corrections in hydrogen-like atoms. The Dirac equation as a quantum system with an infinite number of degrees of freedom.

scholarly journals q-Deformed Relativistic Fermion Scattering

2017 ◽  
Vol 2017 ◽  
pp. 1-9 ◽  
Author(s):  
Hadi Sobhani ◽  
Won Sang Chung ◽  
Hassan Hassanabadi
Keyword(s):  
Quantum Mechanics ◽  
Dirac Equation ◽  
Relativistic Quantum ◽  
Reflection And Transmission Coefficients ◽  
Relativistic Quantum Mechanics ◽  
Scattering Problems ◽  
Reflection And Transmission ◽  
Transmission Coefficients

In this article, after introducing a kind ofq-deformation in quantum mechanics, first,q-deformed form of Dirac equation in relativistic quantum mechanics is derived. Then, three important scattering problems in physics are studied. All results have satisfied what we had expected before. Furthermore, effects of all parameters in the problems on the reflection and transmission coefficients are calculated and shown graphically.

scholarly journals The analogy of equation of rotation in complex plane with the Dirac equation, and its foundation

2018 ◽  
Vol 182 ◽  
pp. 02108
Author(s):  
Mohammed Sanduk
Keyword(s):  
Quantum Mechanics ◽  
Dirac Equation ◽  
Special Relativity ◽  
Relativistic Quantum ◽  
Relativistic Quantum Mechanics ◽  
Position Vector ◽  
Partial Observation ◽  
Complex Vector ◽  
Kinematical Model ◽  
Comparison Table

The Three Wave Hypothesis (TWH) has been proposed by Horodecki in 1981. Sanduk attributed TWH to a classical kinematical model of two rolling circles in 2007. In a previous project in 2012, it is shown that the position vector of a point in a system of two rolling circles can be transformed to a complex vector under the effect of partial observation. The present work tries to develop this concept of transformation. Under this transformation, it is found that the kinematical equations of the motion of point can be transformed to equations analogise the relativistic quantum mechanics equations. Many analogies have been found and are listed in a comparison table. These analogies may sagest that both of the quantum mechanics and the special relativity are emergent, and are of the same origin.

scholarly journals Application of relativistic quantum mechanics in radial problems and E/M equations

2021 ◽  
Vol 1869 (1) ◽  
pp. 012187
Author(s):  
G Y Arygunartha ◽  
N M D Janurianti ◽  
Y P Situmeang
Keyword(s):  
Quantum Mechanics ◽  
Relativistic Quantum ◽  
Relativistic Quantum Mechanics

Stochastic microcausality in relativistic quantum mechanics

1984 ◽  
Vol 14 (9) ◽  
pp. 883-906 ◽  
Author(s):  
D. P. Greenwood ◽  
E. Prugovečki
Keyword(s):  
Quantum Mechanics ◽  
Relativistic Quantum ◽  
Relativistic Quantum Mechanics
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