Show/Hide Menu
Hide/Show Apps
Logout
Türkçe
Türkçe
Search
Search
Login
Login
OpenMETU
OpenMETU
About
About
Open Science Policy
Open Science Policy
Communities & Collections
Communities & Collections
Help
Help
Frequently Asked Questions
Frequently Asked Questions
Guides
Guides
Thesis submission
Thesis submission
MS without thesis term project submission
MS without thesis term project submission
Publication submission with DOI
Publication submission with DOI
Publication submission
Publication submission
Supporting Information
Supporting Information
General Information
General Information
Copyright, Embargo and License
Copyright, Embargo and License
Contact us
Contact us
Loop Representation of Wigner’s Little Groups
Download
10.3390sym9070097.pdf
Date
2017-6-23
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
68
views
62
downloads
Cite This
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 internal symmetry groups. As for the language of group theory, the two-by-two representation is used throughout the paper. While this two-by-two representation is for spin-1/2 particles, it is shown possible to construct the representations for spin-0 particles, spin-1 particles, as well as for higher-spin particles, for both massive and massless cases. It is shown also that the four-by-four Dirac matrices constitute a two-by-two representation of Wigner's little group.
Subject Keywords
Wigner's little groups
,
Lorentz group
,
Gauge transformations
,
Massless Particles
,
Photons; Invariance
,
Rotations
,
Spin
URI
https://hdl.handle.net/11511/51582
Journal
Symmetry
DOI
https://doi.org/10.3390/sym9070097
Collections
Department of Physics, Article
Suggestions
OpenMETU
Core
NILPOTENT LENGTH OF A FINITE SOLVABLE GROUP WITH A FROBENIUS GROUP OF AUTOMORPHISMS
Ercan, Gülin; Ogut, Elif (2014-01-01)
We prove that a finite solvable group G admitting a Frobenius group FH of automorphisms of coprime order with kernel F and complement H such that [G, F] = G and C-CG(F) (h) = 1 for all nonidentity elements h is an element of H, is of nilpotent length equal to the nilpotent length of the subgroup of fixed points of H.
Universal groups of intermediate growth and their invariant random subgroups
Benli, Mustafa Gökhan; Nagnibeda, Tatiana (2015-07-01)
We exhibit examples of groups of intermediate growth with ergodic continuous invariant random subgroups. The examples are the universal groups associated with a family of groups of intermediate growth.
Prime graphs of solvable groups
Ulvi , Muhammed İkbal; Ercan, Gülin; Department of Electrical and Electronics Engineering (2020-8)
If $G$ is a finite group, its prime graph $Gamma_G$ is constructed as follows: the vertices are the primes dividing the order of $G$, two vertices $p$ and $q$ are joined by an edge if and only if $G$ contains an element of order $pq$. This thesis is mainly a survey that gives some important results on the prime graphs of solvable groups by presenting their proofs in full detail.
Wigner rotations and little groups
Baskal, S (Springer Science and Business Media LLC, 2004-01-01)
Wigner's little groups are the subgroups of the Poincare group whose transformations leave the four-momentum of a given particle invariant. For a, relativistic particle in motion the little group is a boosted rotation. On the other hand, the kinematical effect of two non-colinear Lorentz boosts is another boost preceded or followed by a rotation, which is called the Wigner rotation. It is shown that there is always a Wigner rotation for a given little group rotation. The differences between those two rotati...
Centralizers of subgroups in simple locally finite groups
ERSOY, KIVANÇ; Kuzucuoğlu, Mahmut (2012-01-01)
Hartley asked the following question: Is the centralizer of every finite subgroup in a simple non-linear locally finite group infinite? We answer a stronger version of this question for finite K-semisimple subgroups. Namely let G be a non-linear simple locally finite group which has a Kegel sequence K = {(G(i), 1) : i is an element of N} consisting of finite simple subgroups. Then for any finite subgroup F consisting of K-semisimple elements in G, the centralizer C-G(F) has an infinite abelian subgroup A is...
Citation Formats
IEEE
ACM
APA
CHICAGO
MLA
BibTeX
S. Başkal, Y. S. Kim, and M. E. Noz, “Loop Representation of Wigner’s Little Groups,”
Symmetry
, 2017, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/51582.