Particle interpretation of the Dirac–Coulomb solutions

1993 ◽  
Vol 71 (7-8) ◽  
pp. 360-364 ◽  
Author(s):  
Ileana Guiasu ◽  
Roman Koniuk
Keyword(s):  
Quantum Mechanics ◽  
Fock Space ◽  
Relativistic Quantum ◽  
Coulomb Field ◽  
Relativistic Quantum Mechanics ◽  
Pair Annihilation ◽  
Unitary Transformations ◽  
Disconnected Graphs ◽  
Particle Interpretation ◽  
Dirac Hamiltonian

The Dirac Hamiltonian with an external Coulomb field is considered in Fock space; it contains an even part that conserves the number of fermion–antifeimion pairs and an odd part that permits pair annihilation and creation. By successive unitary transformations the nondiagonal terms connecting subspaces with different numbers of pairs can be removed order by order in an (1/m) expansion and the effective no-pair Hamiltonian can be explicitly constructed. If all disconnected graphs are excluded the result is then identical to the result obtained by a similar procedure applied to the Dirac–Coulomb one particle problem in relativistic quantum mechanics.

scholarly journals PSEUDO-HERMITIAN INTERACTIONS IN DIRAC THEORY: EXAMPLES

2010 ◽  
Vol 25 (20) ◽  
pp. 1723-1732 ◽  
Author(s):  
BHABANI PRASAD MANDAl ◽  
SAURABH GUPTA
Keyword(s):  
Quantum Mechanics ◽  
Relativistic Quantum ◽  
Positive Definite ◽  
The Other ◽  
Relativistic Quantum Mechanics ◽  
Arbitrary Parameter ◽  
Scalar Interaction ◽  
Dirac Theory ◽  
Metric Operator ◽  
Dirac Hamiltonian

We consider a couple of examples to study the pseudo-Hermitian interaction in relativistic quantum mechanics. Rasbha interaction, commonly used to study the spin Hall effect, is considered with imaginary coupling. The corresponding Dirac Hamiltonian is shown to be parity pseudo-Hermitian. In the other example we consider parity pseudo-Hermitian scalar interaction with arbitrary parameter in Dirac theory. In both cases we show that the energy spectrum is real and all the other features of nonrelativistic pseudo-Hermitian formulation are present. Using the spectral method, the positive definite metric operator (η) has been calculated explicitly for both the models to ensure positive definite norms for the state vectors.

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

Relativistic Multiple Scattering Theory

1991 ◽  
Vol 253 ◽  
Author(s):  
B. L. Gyorffy
Keyword(s):  
Quantum Mechanics ◽  
Degrees Of Freedom ◽  
Relativistic Quantum ◽  
Schr6dinger Equation ◽  
Relativistic Effects ◽  
Relativistic Quantum Mechanics ◽  
Absolute Minimum ◽  
Crystalline Anisotropy ◽  
Symmetry Properties ◽  
Finite Set

The symmetry properties of the Dirac equation, which describes electrons in relativistic quantum mechanics, is rather different from that of the corresponding Schr6dinger equation. Consequently, even when the velocity of light, c, is much larger than the velocity of an electron Vk, with wave vector, k, relativistic effects may be important. For instance, while the exchange interaction is isotropic in non-relativistic quantum mechanics the coupling between spin and orbital degrees of freedom in relativistic quantum mechanics implies that the band structure of a spin polarized metal depends on the orientation of its magnetization with respect to the crystal axis. As a consequence there is a finite set of degenerate directions for which the total energy of the electrons is an absolute minimum. Evidently, the above effect is the principle mechanism of the magneto crystalline anisotropy [1]. The following session will focus on this and other qualitatively new relativistic effects, such as dichroism at x-ray frequencies [2] or Fano effects in photo-emission from non-polarized solids [3].

scholarly journals PROBABILITY IN RELATIVISTIC QUANTUM MECHANICS AND FOLIATION OF SPACE–TIME

2007 ◽  
Vol 22 (32) ◽  
pp. 6243-6251 ◽  
Author(s):  
HRVOJE NIKOLIĆ
Keyword(s):  
Quantum Mechanics ◽  
Wave Equations ◽  
Integral Curve ◽  
Relativistic Quantum ◽  
Space Time ◽  
Relativistic Quantum Mechanics ◽  
Relativistic Wave ◽  
Probability Densities ◽  
The Many ◽  
Conserved Currents

The conserved probability densities (attributed to the conserved currents derived from relativistic wave equations) should be nonnegative and the integral of them over an entire hypersurface should be equal to one. To satisfy these requirements in a covariant manner, the foliation of space–time must be such that each integral curve of the current crosses each hypersurface of the foliation once and only once. In some cases, it is necessary to use hypersurfaces that are not spacelike everywhere. The generalization to the many-particle case is also possible.

Dirac's aether in relativistic quantum mechanics

1983 ◽  
Vol 13 (2) ◽  
pp. 253-286 ◽  
Author(s):  
Nicola Cufaro Petroni ◽  
Jean Pierre Vigier
Keyword(s):  
Quantum Mechanics ◽  
Relativistic Quantum ◽  
Relativistic Quantum Mechanics
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