Interfacing relativistic and nonrelativistic methods. I. Normalized elimination of the small component in the modified Dirac equation

1997 ◽  
Vol 106 (23) ◽  
pp. 9618-9626 ◽  
Author(s):  
Kenneth G. Dyall
Keyword(s):  
Dirac Equation ◽  
Small Component ◽  
Modified Dirac Equation

scholarly journals INFLUENCE OF GRAVITY ON NONCOMMUTATIVE DIRAC EQUATION

2005 ◽  
Vol 20 (26) ◽  
pp. 1997-2005 ◽  
Author(s):  
SOFIANE BOUROUAINE ◽  
ACHOUR BENSLAMA
Keyword(s):  
Dirac Equation ◽  
Electric Field ◽  
Covariant Derivative ◽  
Strong Electric Field ◽  
Curved Spacetime ◽  
Tetrad Formalism ◽  
Dirac Particles ◽  
Modified Dirac Equation ◽  
New Form

In this paper, we investigate the influence of gravity and noncommutativity on Dirac particles. By adopting the tetrad formalism, we show that the modified Dirac equation keeps the same form. The only modification is in the expression of the covariant derivative. The new form of this derivative is the product of its counterpart given in curved spacetime with an operator which depends on the noncommutative θ-parameter. As an application, we have computed the density number of the created particles in the presence of constant strong electric field in an anisotropic Bianchi universe.

Modified Dirac Equation

2008 ◽  
pp. 47-107
Author(s):  
Henning F. Harmuth ◽  
Beate Meffert
Keyword(s):  
Dirac Equation ◽  
Modified Dirac Equation

scholarly journals Rigorous Derivation of the Pauli Equation With Time-dependent Electromagnetic Field

VLSI Design ◽  
1999 ◽  
Vol 9 (4) ◽  
pp. 415-426 ◽  
Author(s):  
Norbert J. Mauser
Keyword(s):  
Dirac Equation ◽  
Order Approximation ◽  
Fundamental Equation ◽  
Time Dependent ◽  
Projection Operators ◽  
Rigorous Derivation ◽  
Solid State Physics ◽  
Pauli Equation ◽  
Rigorous Results ◽  
Small Component

In this work we discuss relativistic corrections for the description of charge carriers in a quantum mechanical framework. The fundamental equation is the Dirac equation which takes into account also the electron's spin. However, this equation intrinsically also incorporates positrons which play no role in applications in solid state physics. We give a rigorous derivation of the Pauli equation describing electrons in a first order approximation of the Dirac equation in the limit of infinite velocity of light. We deal with time-dependent electromagnetic potentials where no rigorous results have been given before. Our approach is based on the use of appropriate projection operators for the electron and the positron component of the spinor which are better suited than the widely used simple splitting into ‘upper (large)’ and ‘lower (small) component’. We also systematically derive corrections at second order in 1/c where we essentially recover the results of the Foldy-Wouthuysen approach. However, due to the non-static problem, differences occur in the term which couples the electric field with the spin.

AN ULTRA HIGH ENERGY DIRAC EQUATION

2005 ◽  
Vol 14 (06) ◽  
pp. 927-929 ◽  
Author(s):  
B. G. SIDHARTH
Keyword(s):  
Dirac Equation ◽  
Planck Scale ◽  
High Energy ◽  
Ultra High Energy ◽  
High Energy Cosmic Rays ◽  
High Energies ◽  
Discrete Spacetime ◽  
Modified Dirac Equation ◽  
Very High ◽  
Momentum Relation

Violations in Lorentz symmetry at very high energies are being discussed by Glashow, Coleman, the author and others. The motivation comes from certain observed events pertaining to ultra high energy cosmic rays, and also from theoretical quantum gravity studies, which require a discrete spacetime at the Planck scale. We examine the modification to the usual energy momentum relation, and in light of this, deduce a modified Dirac equation and examine some consequences.

Black hole remnant and quantum tunneling corrections to the five-dimensional Myers–Perry black hole based on generalized uncertainty principle

2016 ◽  
Vol 94 (11) ◽  
pp. 1153-1157 ◽  
Author(s):  
Hui-Ling Li ◽  
Rong Lin
Keyword(s):  
Black Hole ◽  
Dirac Equation ◽  
Quantum Gravity ◽  
Quantum Tunneling ◽  
Generalized Uncertainty Principle ◽  
Tunneling Probability ◽  
Gravity Effect ◽  
Quantum Gravity Effect ◽  
Modified Dirac Equation ◽  
Black Hole Remnant

Taking into account quantum gravity effect influenced by the generalized uncertain principle (GUP), via modified Dirac equation, we discuss the quantum gravity correction to fermion tunneling and the remnant in a five-dimensional Myers–Perry black hole. By analyzing the modified tunneling probability, we find that the emission spectrum is no longer pure thermal. Furthermore, it is worth emphasizing that the quantum gravity correction influenced by GUP prevents the black hole from evaporating totally, resulting in a black hole remnant.

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