The Dirac Equation as One Fourth-Order Equation for One Function: A General, Manifestly Covariant Form

@article{Akhmeteli2018TheDE,
  title={The Dirac Equation as One Fourth-Order Equation for One Function: A General, Manifestly Covariant Form},
  author={Andrey Akhmeteli},
  journal={arXiv: Quantum Physics},
  year={2018},
  pages={1-11}
}
  • A. Akhmeteli
  • Published 9 February 2015
  • Physics
  • arXiv: Quantum Physics
Previously (A. Akhmeteli, J. Math. Phys., v. 52, p. 082303 (2011)), the Dirac equation in an arbitrary electromagnetic field was shown to be generally equivalent to a fourth-order equation for just one component of the four-component Dirac spinor function. This was done for a specific (chiral) representation of gamma matrices and for a specific component. In the current work, the result is generalized for a general representation of gamma matrices and a general component (satisfying some… 
2 Citations

Plasma-like Description for Elementary and Composite Quantum Particles

Schrödinger noticed in 1952 that a scalar complex wave function can be made real by a gauge transformation. The author showed recently that one real function is also enough to describe matter in the

Squaring the Dirac Equations

A complete solution of the problem of squaring the Dirac equation with arbitrary external electromagnetic field is expounded.

References

SHOWING 1-10 OF 20 REFERENCES

One real function instead of the Dirac spinor function

Three out of four complex components of the Dirac spinor can be algebraically eliminated from the Dirac equation (if some linear combination of electromagnetic fields does not vanish), yielding a

The Dirac Equation and Its' Solutions

The Dirac equation is of fundamental importance for relativistic quantum mechanics and quantum electrodynamics, representing the one-particle wave equation of motion for electrons in an external

Theory of the Fermi Interaction

The representation of Fermi particles by two-component Pauli spinors satisfying a second order differential equation and the suggestion that in β decay these spinors act without gradient couplings

The quantum theory of the electron

The new quantum mechanics, when applied to the problem of the structure of the atom with point-charge electrons, does not give results in agreement with experiment. The discrepancies consist of

Introduction to the theory of quantized fields

This site is also available in the following languages: Български Català Deutsch Ελληνικά English Español Français Hrvatski Italiano Norsk/Bokmål Polski Português Русский Slovensky Svenska ( ) ( )

Relativity and the lead-acid battery.

The energies of the solid reactants in the lead-acid battery are calculated ab initio using two different basis sets at nonrelativistic, scalar-relativistic, and fully relativistic levels, and using

Phys 52

  • 082303
  • 2011

The Dirac Equation

I and i

TLDR
There is, I think, something ethereal about i —the square root of minus one, which seems an odd beast at that time—an intruder hovering on the edge of reality.