Lorentz group in polarization optics

Download

index.pdf

Date

2012

Author

Oktay, Onur

Metadata

Show full item record

Item Usage Stats

93
views

67
downloads

The group theory allows one to study different branches of physics using the same set of commutation relations. It is shown that a formulation of the polarization optics that depends on the representations of the Lorentz group is possible. The set of four Stokes parameters, which is a standard tool of polarization optics, can be used to form a four-vector that is physically unrelated but mathematically equivalent to the space-time four-vector of the special relativity. By using the Stokes parameters, it is also possible to generate four-by-four matrix representations of the ordinary optical filters that are traditionally represented with the two-by-two Jones matrices. These four-by-four matrices are treated as the entities of the Lorentz group. They are like the Lorentz transformations applicable to the four-dimensional polarization space. Besides, optical decoherence process can be formulated within the framework of the SO(3,2) de Sitter group. The connection between the classical and quantum mechanical descriptions of the polarization of light allows the extension of the Stokes parameters to the quantum domain. In this respect, the properties of the polarization of the two-photon system can also be studied within the framework of the Lorentz group.

Subject Keywords

Lorentz groups., Optics., Polarization (Light).

URI

http://etd.lib.metu.edu.tr/upload/12614773/index.pdf
https://hdl.handle.net/11511/21932

Collections

Graduate School of Natural and Applied Sciences, Thesis

Suggestions

OpenMETU
Core

Algebraic curves hermitian lattices and hypergeometric functions Zeytin, Ayberk; Önsiper, Mustafa Hurşit; Department of Mathematics (2011) The aim of this work is to study the interaction between two classical objects of mathematics: the modular group, and the absolute Galois group. The latter acts on the category of finite index subgroups of the modular group. However, it is a task out of reach do understand this action in this generality. We propose a lattice which parametrizes a certain system of ”geometric” elements in this category. This system is setwise invariant under the Galois action, and there is a hope that one can explicitly under...
Entangled Harmonic Oscillators and Space-Time Entanglement Başkal, Sibel; Kim, Young S.; Noz, Marilyn E. (MDPI AG, 2016-6-28) 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. It is shown that the Gaussian entanglement shares the same set of mathematical formulas with the harmonic oscillator in the Lorentz-covariant world. It is thus possible to transfer the concept of entanglement to the Lorentz-covariant picture of the bound state, which requires both space and time separations between two constituent p...
Nonlocal regularisation of noncommutative field theories Govindarajan, T. R.; Kürkcüoğlu, Seçkin; PANERO, Marco (World Scientific Pub Co Pte Lt, 2006-08-10) We study noncommutative field theories, which are inherently nonlocal, using a Poincare-invariant regularisation scheme which yields an effective, nonlocal theory for energies below a cutoff scale. After discussing the general features and the peculiar advantages of this regularisation scheme for theories defined in noncommutative spaces, we focus our attention on the particular case when the noncommutativity parameter is inversely proportional to the square of the cutoff, via a dimensionless parameter eta....
Loop Representation of Wigner’s Little Groups Başkal, Sibel; Kim, Young S.; Noz, Marilyn E (MDPI AG, 2017-6-23) Wigner's little groups are the subgroups of the Lorentz group whose transformations leave the momentum of a given particle invariant. They thus define the internal space-time symmetries of relativistic particles. These symmetries take different mathematical forms for massive and for massless particles. However, it is shown possible to construct one unified representation using a graphical description. This graphical approach allows us to describe vividly parity, time reversal, and charge conjugation of the ...
Centralizers of finite subgroups in Hall's universal group Kegel, Otto H.; Kuzucuoğlu, Mahmut (2017-01-01) The structure of the centralizers of elements and finite abelian subgroups in Hall's universal group is studied by B. Hartley by using the property of existential closed structure of Hall's universal group in the class of locally finite groups. The structure of the centralizers of arbitrary finite subgroups were an open question for a long time. Here by using basic group theory and the construction of P. Hall we give a complete description of the structure of centralizers of arbitrary finite subgroups in Ha...

Citation Formats

O. Oktay, “Lorentz group in polarization optics,” M.S. - Master of Science, Middle East Technical University, 2012.