Poincaré Symmetry from Heisenberg’s Uncertainty Relations

Download

19.pdf

Date

2019-3-20

Author

Başkal, Sibel
Kim , Young S.
Noz, Marilyn E

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

78
views

106
downloads

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 two space-like dimensions, known as the S O ( 2 , 1 ) group. According to Paul A. M. Dirac, from the uncertainty commutation relations for two variables, it possible to construct the de Sitter group S O ( 3 , 2 ) , namely the Lorentz group applicable to three space-like variables and two time-like variables. By contracting one of the time-like variables in S O ( 3 , 2 ) , it is possible to construct the inhomogeneous Lorentz group I S O ( 3 , 1 ) which serves as the fundamental symmetry group for quantum mechanics and quantum field theory in the Lorentz-covariant world. This I S O ( 3 , 1 ) group is commonly known as the Poincaré group.

Subject Keywords

Computer Science (miscellaneous), Physics and Astronomy (miscellaneous), Chemistry (miscellaneous), General Mathematics

URI

https://hdl.handle.net/11511/51652

Journal

Symmetry

DOI

https://doi.org/10.3390/sym11030409

Collections

Department of Physics, Article

Suggestions

OpenMETU
Core

Lepton flavor violating Z -> l(1)(+)l(2)(-) decay in the two Higgs doublet model with the inclusion of non-universal extra dimensions Iltan, EO (Springer Science and Business Media LLC, 2005-05-01) We predict the branching ratios of the Z -> e(+/-) mu(+/-), Z -> e(+/-) tau(+/-) and Z -> mu(+/-)tau(+/-) decays in the model III version of the two Higgs doublet model, with the inclusion of one and two spatial non-universal extra dimensions. We observe that the branching ratios are not sensitive to a single extra dimension, however, this sensitivity is considerable for two extra dimensions.
Charged lepton electric dipole moments with localized leptons and new Higgs doublet in the two Higgs doublet model Iltan, E. O. (Springer Science and Business Media LLC, 2007-08-01) We study the electric dipole moments of the leptons in the split fermion scenario, in the two Higgs doublet model, where the new Higgs scalars are localized around the origin in the extra dimension, with the help of the localizer field. We observe that the numerical value of the electric dipole moment of the electron (muon, tau) is of the order of the magnitude of 10(-31) ( 10(-24), 10(-22)) (e cm), and this quantity is sensitive to the new Higgs localization in the extra dimension.
Lepton flavor violating Z-boson decays induced by scalar unparticle Iltan, E. O. (Springer Science and Business Media LLC, 2008-07-01) We predict the branching ratios of the lepton-flavor violating Z-boson decays Z -> e(+/-)mu(+/-), Z -> e(+/-)tau(+/-) and Z -> mu +/-tau +/- in the case that the lepton-flavor violation is carried by scalar unparticlemediation. We observe that their BRs are strongly sensitive to the unparticle scaling dimension, and the branching ratios can reach values of the order of 10(-8), for the heavy lepton-flavor case, for small values of the scaling dimension.
Lepton flavor violating Zeta -> l(1)(+)l(2)(-) decay in the split fermion scenario in the two Higgs doublet model Iltan, E. O. (Springer Science and Business Media LLC, 2006-05-01) We predict the branching ratios of the Z -> e(+/-)mu(+/-), Z -> e(+/-)tau(+/-) and Z -> mu(+/-)tau(+/-) decays in the framework of the 2HDM, in the split fermion scenario. We observe that the branching ratios are not sensitive to a single extra dimension; however, this sensitivity is considerably large for two extra dimensions.
Spherically symmetric solutions of Einstein plus non-polynomial gravities Deser, S.; Sarıoğlu, Bahtiyar Özgür; Tekin, Bayram (Springer Science and Business Media LLC, 2008-01-01) We obtain the static spherically symmetric solutions of a class of gravitational models whose additions to the General Relativity (GR) action forbid Ricci-flat, in particular, Schwarzschild geometries. These theories are selected to maintain the (first) derivative order of the Einstein equations in Schwarzschild gauge. Generically, the solutions exhibit both horizons and a singularity at the origin, except for one model that forbids spherical symmetry altogether. Extensions to arbitrary dimension with a cos...

Citation Formats

S. Başkal, Y. S. Kim, and M. E. Noz, “Poincaré Symmetry from Heisenberg’s Uncertainty Relations,” Symmetry, 2019, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/51652.