Jones-matrix formalism as a representation of the Lorentz group

Journal of the Optical Society of America A: Optics and Image Science, and Vision

Volumn 14, Issue 9, 1997, Pages 2290-2298

  Han, D ^a   Kim, Y S ^b   Noz, Marilyn E ^c  

^a NASA GODDARD SPACE FLIGHT CENTER   (United States)

^b University of Maryland   (United States)

^c NEW YORK UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000881252     PISSN: 10847529     EISSN: 15208532     Source Type: Journal    
DOI: 10.1364/JOSAA.14.002290     Document Type: Article

References (37)

1. E. Wigner, “On unitary representations of the inhomogeneous Lorentz group,” Ann. Math. 40, 149-204 (1939).
2. V. Bargmann, “Irreducible unitary representations of the Lorentz group,” Ann. Math. 48, 568-640 (1947).
3. P. A. M. Dirac, “Forms of relativistic dynamics,” Rev. Mod. Phys. 21, 392-399 (1949).
4. P. A. M. Dirac, “A remarkable representation of the 3 + 2 de Sitter group,” J. Math. Phys. 4, 901-909 (1963).
5. H. P. Yuen, “Two-photon coherent states of the radiation fields,” Phys. Rev. A 13, 2226-2243 (1976).
6. C. M. Caves and B. L. Schumaker, “New formalism for two photon quantum optics. I. Quadrature phases and squeezed light,” Phys. Rev. A 31, 3068-3092 (1985);
7. B. L. Schumaker and C. M. Caves, “New formalism for two photon quantum optics. II. Mathematical foundation and compact notation,” Phys. Rev. A 31, 3093-3111 (1985).
8. Y. S. Kim and M. E. Noz, Phase Space Picture of Quantum Mechanics (World Scientific, Singapore, 1991), pp. 77-122.
9. H. Bacry and M. Cadilhac, “Metaplectic group and Fourier optics,” Phys. Rev. A 23, 2533-2536 (1981).
10. E. C. G. Sudarshan, R. Simon, and N. Makunda, “Paraxial-wave optics and relativistic front description. I. The scalar theory,” Phys. Rev. A 28, 2921-2932 (1983);
11. N. Makunda, R. Simon, and E. C. G. Sudarshan, “Paraxial-wave optics and relativistic front description. II. The vector theory,” Phys. Rev. A 28, 2933-2942 (1983).
12. D. Han, Y. S. Kim, and M. E. Noz, “Wavelets, windows, and photons,” Phys. Lett. A 206, 299-304 (1995).
13. P. Pellat-Finet and M. Buasset, “What is common to both polarization optics and relativistic kinematics?" Optik (Stuttgart) 90, 101-106 (1992).
14. M. Gutierrez, J. C. Minano, C. Vega, and P. Benitez, “Application of Lorentz geometry to non-imaging optics: new three-dimensional ideal contractors,” J. Opt. Soc. Am. A 13, 532-542 (1996).
15. S. R. Cloude, “Group theory and polarization algebra,” Optik 75, 26-36 (1986).
16. R. Y. Chiao and T. F. Jordan, “Lorentz-group Berry phases in squeezed light,” Phys. Lett. A 132, 77-81 (1988).
17. M. Kitano and T. Yabuzaki, “Observation of Lorentz-group Berry phases in polarization optics,” Phys. Lett. A 142, 321-325 (1989).
18. T. Opatrny and J. Perina, “Non-image-forming polarization optical devices and Lorentz transformations-analogy,” Phys. Lett. A 181, 199-202 (1993).
19. D. Han, Y. S. Kim, and M. E. Noz, “Polarization optics and bilinear representation of the Lorentz group,” Phys. Lett. A 219, 26-32 (1996).
20. R. C. Jones, “New calculus for the treatment of optical systems,” J. Opt. Soc. Am. 31, 488-493 (1941).
21. W. Swindell, Polarized Light (Dowden, Hutchinson, and Ross, Stroudsburg, Pa., 1975).
22. F. L. Pedrotti and L. S. Pedrotti, Introduction to Optics, 2nd ed. (Prentice-Hall, Englewood Cliffs, N. J., 1993), pp. 280-297.
23. D. Han, Y. S. Kim, and D. Son, “E(2)-like little group for massless particles and polarization of neutrinos,” Phys. Rev. D 26, 3717-3725 (1982).
24. Y. S. Kim and L. Yeh, “E(2)-symmetric sheared states,” J. Math. Phys. 33, 1237-1246 (1992).
25. A. S. Chirkin, A. A. Orlov, and D. Yu. Parashchuk, “Quantum theory of two-mode interactions in optically anisotropic media with cubic nonlinearities: generation of quadrature-and polarization-squeezed light,” Quantum Electron. 23, 870-874 (1993).
26. R. Abraham and J. E. Marsden, Foundations of Mechanics, 2nd ed. (Benjamin/Cummings, Reading, Mass., 1978).
27. V. Guillemin and S. Sternberg, Symplectic Techniques in Physics (Cambridge U. Press, Cambridge, 1984).
28. Y. S. Kim and M. E. Noz, Theory and Applications of the Poincare Group (Reidel, Dordrecht, The Netherlands, 1986).
29. G. P. Parent and P. Roman, “On the matrix formulation of the theory of partial polarization in terms of observables,” Nuovo Cimento 15, 370-388 (1960);
30. R. Barakat, “Theory of the coherency matrix for light of arbitrary bandwidth,” J. Opt. Soc. Am. 53, 317-323 (1963);
31. H. Takenaka, “A unified formalism for polarization optics by using group theory,” Nouv. Res. Opt. 4, 37-41 (1973).
32. C. E. Baum and H. N. Kritikos, Electromagnetic Symmetry (Taylor & Francis, Washington, D.C., 1995).
33. M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1980), pp. 545-553.
34. J. Perina, Coherence of Light (Van Nostrand-Reinhold, London, 1971), pp. 77-88.
35. D. Han, Y. S. Kim, and D. Son, “Photons, neutrinos, and gauge transformations,” Am. J. Phys. 54, 818-821 (1986).
36. S. Baskal and Y. S. Kim, “Four-potentials and Maxwell field tensors from SL(2, C) spinors as infinite-momentum/zero-mass limits of their massive counterparts,” Los Alamos E-print Archive hep-th/9512088 (Los Alamos National Laboratory, Los Alamos, N. Mex., 1995).
37. S. Weinberg, “Feynman rules for any spin II massless particles." Phys. Rev. 134, B882-B896 (1964).