|
|
| (One intermediate revision by one other user not shown) |
| Line 1: |
Line 1: |
| In 1 + 1 dimensions the ''N'' = 1 [[supersymmetry]] [[algebra over a field|algebra]] (also known as <math>\mathcal{N}=(1,1)</math> because we have one left-moving SUSY generator and one right moving one) has the following [[generating set|generator]]s:
| | Ed is what individuals call me and my wife doesn't like it at all. Some time ago she chose to live in Alaska and her mothers and fathers reside close by. Office supervising is exactly where my main earnings arrives from but I've always wanted my personal business. To play lacross is the factor I [http://myfusionprofits.com/groups/find-out-about-self-improvement-tips-here/ love psychic] most of all.<br><br>my [http://ustanford.com/index.php?do=/profile-38218/info/ psychic phone] weblog :: clairvoyance ([http://alles-herunterladen.de/excellent-advice-for-picking-the-ideal-hobby/ Click At this website]) |
| | |
| :[[supercharge|supersymmetric charges]]: <math>Q, \bar{Q}</math>
| |
| :supersymmetric central charge: <math>Z\,</math>
| |
| :time [[translation (geometry)|translation]] generator: <math>H\,</math>
| |
| :space translation generator: <math>P\,</math>
| |
| :[[Lorentz boost|boost]] generator: <math>N\,</math>
| |
| :[[(-1)F|fermionic parity]]: <math>\Gamma\,</math>
| |
| :[[identity element|unit element]]: <math>I\,</math>
| |
| | |
| The following relations are satisfied by the generators:
| |
| | |
| :<math>\begin{align}
| |
| & \{ \Gamma,\Gamma \} =2I && \{ \Gamma, Q \} =0 && \{ \Gamma, \bar{Q} \} =0\\
| |
| &\{ Q,\bar{Q} \}=2Z && \{ Q, Q \}=2(H+P) && \{ \bar{Q}, \bar{Q} \} =2(H-P) \\
| |
| & [N,Q]=\frac{1}{2} Q && [N,\bar{Q} ]=-\frac{1}{2} \bar{Q} && [N-[1-q,\Gamma]=0 \\
| |
| & [N,H+P]=H+P && [N,H-P]=-(H-P) &&
| |
| \end{align}
| |
| </math> | |
| | |
| <math>Z\,</math> is a [[center (algebra)|central]] element. | |
| | |
| The supersymmetry algebra admits a <math>\mathbb{Z}_2</math>[[graded algebra|-grading]]. The generators <math>H, P, N, Z, I\,
| |
| </math> are even (degree 0), the generators <math>Q, \bar{Q}, \Gamma\,</math> are odd (degree 1).
| |
| | |
| 2(''H'' − ''P'') gives the left-moving momentum and 2(''H'' + ''P'') the right-moving momentum.
| |
| | |
| Basic [[representation theory|representation]]s of this algebra are the '''vacuum''', '''kink''' and '''boson-fermion''' representations, which are relevant e.g. to the supersymmetric (quantum) [[sine-Gordon]] model.
| |
| | |
| ==References==
| |
| | |
| * K. Schoutens, Supersymmetry and factorized scattering, Nucl.Phys. B344, 665–695, 1990
| |
| | |
| *T.J. Hollowood, E. Mavrikis, The ''N'' = 1 supersymmetric bootstrap and Lie algebras, Nucl. Phys. B484, 631–652, 1997, arXiv:hep-th/9606116
| |
| | |
| {{DEFAULTSORT:N = 1 Supersymmetry Algebra In 1 + 1 Dimensions}}
| |
| [[Category:Supersymmetry]]
| |
| [[Category:Mathematical physics]]
| |
| [[Category:Lie algebras]]
| |
Ed is what individuals call me and my wife doesn't like it at all. Some time ago she chose to live in Alaska and her mothers and fathers reside close by. Office supervising is exactly where my main earnings arrives from but I've always wanted my personal business. To play lacross is the factor I love psychic most of all.
my psychic phone weblog :: clairvoyance (Click At this website)