# Role of Quantum Optics in Synthesizing Quantum Mechanics and Relativity

@article{Kim2019RoleOQ, title={Role of Quantum Optics in Synthesizing Quantum Mechanics and Relativity}, author={Y. S. Kim}, journal={arXiv: Quantum Physics}, year={2019} }

Two-photon states produce enough symmetry needed for Dirac's construction of the two-oscillator system which produces the Lie algebra for the O(3,2) space-time symmetry. This O(3,2) group can be contracted to the inhomogeneous Lorentz group which, according to Dirac, serves as the basic space-time symmetry for quantum mechanics in the Lorentz-covariant world. Since the harmonic oscillator serves as the language of Heisenberg's uncertainty relations, it is right to say that the symmetry of the…

## Figures and Tables from this paper

## References

SHOWING 1-10 OF 15 REFERENCES

Physics of the Lorentz Group

- Physics, Education
- 2015

This book explains the Lorentz mathematical group in a language familiar to physicists. While the three-dimensional rotation group is one of the standard mathematical tools in physics, the Lorentz…

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…

Forms of Relativistic Dynamics

- Physics
- 1949

For the purposes of atomic theory it is necessary to combine the restricted principle of relativity with the Hamiltonian formulation of dynamics. This combination leads to the appearance of ten…

Two-photon coherent states of the radiation field

- Physics
- 1976

The concept of a two-photon coherent state is introduced for applications in quantum optics. It is a simple generalization of the well-known minimum-uncertainty wave packets. The detailed properties…

On the Contraction of Groups and Their Representations.

- MathematicsProceedings of the National Academy of Sciences of the United States of America
- 1953

The purpose of the present note is to investigate, in some generality, in which sense groups can be limiting cases of other groups, and how their representations can be obtained from the representations of the groups of which they appear as limits.

Unitary representations of the Lorentz group

- MathematicsProceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences
- 1945

Certain quantities are introduced which are like tensors in space-time with an infinite enumerable number of components and with an invariant positive definite quadratic form for their squared…

Unitary representations of the inhomogeneous Lorentz group

- Physics
- 1964

SummaryA realization of the unitary representation [m, s] of the inhomogeneous Lorentz group is derived, in the case of nonzero mass, which has simple transformation properties yet has no superfluous…

SU(2) and SU(1,1) interferometers.

- PhysicsPhysical review. A, General physics
- 1986

A Lie-group-theoretical approach to the analysis of interferometers is presented. Conventional interferometers such as the Mach-Zehnder and Fabry-Perot can be characterized by SU(2). We introduce a…

Dashen-Frautschi Fiasco and Historical Roadmap for Strings

- Physics
- 2004

In 1964, Dashen and Frautschi published two papers in the Physical Review claiming that they calculated the neutron-proton mass difference. It was once regarded as a history-making calculation, in…