Английская Википедия:Adinkra symbols (physics)
In supergravity and supersymmetric representation theory, Adinkra symbols are a graphical representation of supersymmetric algebras.[1][2][3][4][5] Mathematically they can be described as colored finite connected simple graphs, that are bipartite and n-regular.[6] Their name is derived from Adinkra symbols of the same name, and they were introduced by Michael Faux and Sylvester James Gates in 2004.[1]
Overview
One approach to the representation theory of super Lie algebras is to restrict attention to representations in one space-time dimension and having <math> N </math> supersymmetry generators, i.e., to <math> (1|N) </math> superalgebras. In that case, the defining algebraic relationship among the supersymmetry generators reduces to
- <math>\{Q_I, Q_J\} = 2 i \delta _{I J} \partial_\tau </math>.
Here <math> \partial_\tau </math> denotes partial differentiation along the single space-time coordinate. One simple realization of the <math> (1|1) </math> algebra consists of a single bosonic field <math> \phi </math>, a fermionic field <math> \psi </math>, and a generator <math> Q </math> which acts as
- <math> Q \phi= i \psi </math>,
- <math> Q \psi= \partial_\tau \phi</math>.
Since we have just one supersymmetry generator in this case, the superalgebra relation reduces to <math> Q^2 = i \partial _\tau </math>, which is clearly satisfied. We can represent this algebra graphically using one solid vertex, one hollow vertex, and a single colored edge connecting them.
See also
References
External links
- http://golem.ph.utexas.edu/category/2007/08/adinkras.html
- https://www.flickr.com/photos/science_and_thecity/2796684536/
- https://www.flickr.com/photos/science_and_thecity/2795836787/
- http://www.thegreatcourses.com/courses/superstring-theory-the-dna-of-reality.html
- ↑ 1,0 1,1 Шаблон:Cite journal
- ↑ S. James Gates Jr.: "Superstring Theory: The DNA of Reality Шаблон:Webarchive" (The Teaching Company)
- ↑ S.J. Gates, Jr.: "Symbols of Power, Physics World, Vol. 23, No 6, June 2010, pp. 34 - 39" Шаблон:Webarchive
- ↑ S.J. Gates, Jr.: "Quarks to Cosmos Шаблон:Webarchive"
- ↑ S.J. Gates, Jr., and T. Hubsch, "On Dimensional Extension of Supersymmetry: From Worldlines to Worldsheets"
- ↑ Шаблон:Cite arXiv
