# Stokes Parameters as a Minkowskian Four-vector

@article{Han1997StokesPA, title={Stokes Parameters as a Minkowskian Four-vector}, author={D. Han and Y. S. Kim and M. Noz}, journal={Physical Review E}, year={1997}, volume={56}, pages={6065-6076} }

It is noted that the Jones-matrix formalism for polarization optics is a six-parameter two-by-two representation of the Lorentz group. It is shown that the four independent Stokes parameters form a Minkowskian four-vector, just like the energy-momentum four-vector in special relativity. The optical filters are represented by four-by-four Lorentz-transformation matrices. This four-by-four formalism can deal with partial coherence described by the Stokes parameters. A four-by-four matrix…

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## References

SHOWING 1-10 OF 35 REFERENCES

Four-potentials and Maxwell Field Tensors from $SL(2,C)$ Spinors as Infinite-Momentum/Zero-Mass Limits of their Massive Counterparts

- Physics
- 1995

Four $SL(2,C)$ spinors are considered within the framework of Wigner's little groups which dictate internal space-time symmetries of relativistic particles. It is indicated that the little group for…

Phase Space Picture of Quantum Mechanics: Group Theoretical Approach

- Physics
- 1991

This book covers the theory and applications of the Wigner phase space distribution function and its symmetry properties. The book explains why the phase space picture of quantum mechanics is needed,…

Theory and Applications of the Poincaré Group

- Physics, Mathematics
- 1986

I: Elements of Group Theory.- 1. Definition of a Group.- 2. Subgroups, Cosets, and Invariant Subgroups.- 3. Equivalence Classes, Orbits, and Little Groups.- 4. Representations and Representation…

Phys

- Lett. A 206, 299
- 1996

Shurcliff, Polarized Light (Harvard

- 1962

Phys. Lett. A

- Phys. Lett. A
- 1996

J. Math. Phys

- J. Math. Phys
- 1995

J. Math. Phys

- J. Math. Phys
- 1992

Optik (Stuttgart)

- Optik (Stuttgart)
- 1992

Phys

- 33, 1237
- 1992