# Integration of Dirac's Efforts to construct Lorentz-covariant Quantum Mechanics

@article{Kim2020IntegrationOD, title={Integration of Dirac's Efforts to construct Lorentz-covariant Quantum Mechanics}, author={Young S. Kim and M. Noz}, journal={arXiv: Quantum Physics}, year={2020} }

The lifelong efforts of Paul A. M. Dirac were to construct localized quantum systems in the Lorentz covariant world. In 1927, he noted that the time-energy uncertainty should be included in the Lorentz-covariant picture. In 1945, he attempted to construct a representation of the Lorentz group using a normalizable Gaussian function localized both in the space and time variables. In 1949, he introduced his instant form to exclude time-like oscillations. He also introduced the light-cone…

## Figures and Tables from this paper

## References

SHOWING 1-10 OF 67 REFERENCES

Entangled Harmonic Oscillators and Space-Time Entanglement

- PhysicsSymmetry
- 2016

The mathematical basis for the Gaussian entanglement is discussed in detail, as well as its implications in the internal space-time structure of relativistic extended particles and the shear transformation is an interesting future possibility.

Representations of the Poincaré group for relativistic extended hadrons

- Physics
- 1979

Representations of the Poincare group are constructed from the relativistic harmonic oscillator wave functions which have been effective in describing the physics of internal quark motions in the…

Poincaré Symmetry from Heisenberg's Uncertainty Relations

- PhysicsSymmetry
- 2019

It is noted that the single-variable Heisenberg commutation relation contains the symmetry of the S p ( 2 ) group which is isomorphic to the Lorentz group applicable to one time-like dimension and…

The Quantum Theory of the Emission and Absorption of Radiation

- Physics
- 1927

The new quantum theory, based on the assumption that the dynamical variables do not obey the commutative law of multiplication, has by now been developed sufficiently to form a fairly complete theory…

Covariant Harmonic Oscillators and the Quark Model

- Physics
- 1973

An attempt is made to give a physical interpretation to the phenomenological wave function of Yukawa, which gives a correct nucleon form factor in the symmetric quark model. This wave function is…

Space-time geometry of relativistic particles

- Physics
- 2014

A three-dimensional space-time geometry of relativistic particles is constructed within the framework of the little groups of the Poincaré group. Since the little group for a massive particle is the…

Physical principles in quantum field theory and in covariant harmonic oscillator formalism

- Physics
- 1981

It is shown that both covariant harmonic oscillator formalism and quantum field theory are based on common physical principles which include Poincaré covariance, Heisenberg's space-momentum…

Einstein’s E=mc2 Derivable from Heisenberg’s Uncertainty Relations

- Mathematics, PhysicsQuantum Reports
- 2019

Heisenberg’s uncertainty relation can be written in terms of the step-up and step-down operators in the harmonic oscillator representation. It is noted that the single-variable Heisenberg commutation…

Coupled oscillators, entangled oscillators, and Lorentz-covariant harmonic oscillators

- Physics, Education
- 2005

Other than scattering problems where perturbation theory is applicable, there are basically two ways to solve problems in physics. One is to reduce the problem to harmonic oscillators, and the other…

A simple method for illustrating the difference between the homogeneous and inhomogeneous Lorentz groups

- Physics, Mathematics
- 1979

A method is proposed for illustrating the difference between the Poincare (inhomogeneous Lorentz) and homogeneous Lorentz groups. Representations of the Poincare group are constructed from solutions…