The Meaning of Time and Covariant Superderivatives in Supermechanics
Joint Authors
Vallejo-Rodríguez, José A.
Salgado, Gil
Source
Advances in Mathematical Physics
Issue
Vol. 2009, Issue 2009 (31 Dec. 2009), pp.1-21, 21 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2009-07-02
Country of Publication
Egypt
No. of Pages
21
Main Subjects
Abstract EN
We present a review of the basics of supermanifold theory (in the sense of Berezin-Kostant-Leites-Manin) from a physicist's point of view.
By considering a detailed example of what does it mean the expression “to integrate an ordinary superdifferential equation” we show how the appearance of anticommuting parameters playing the role of time is very natural in this context.
We conclude that in dynamical theories formulated whithin the category of supermanifolds, the space that classically parametrizes time (the real line ℝ) must be replaced by the simplest linear supermanifold ℝ1|1.
This supermanifold admits several different Lie supergroup structures, and we analyze from a group-theoretic point of view what is the meaning of the usual covariant superderivatives, relating them to a change in the underlying group law.
This result is extended to the case of N-supersymmetry.
American Psychological Association (APA)
Salgado, Gil& Vallejo-Rodríguez, José A.. 2009. The Meaning of Time and Covariant Superderivatives in Supermechanics. Advances in Mathematical Physics،Vol. 2009, no. 2009, pp.1-21.
https://search.emarefa.net/detail/BIM-513912
Modern Language Association (MLA)
Salgado, Gil& Vallejo-Rodríguez, José A.. The Meaning of Time and Covariant Superderivatives in Supermechanics. Advances in Mathematical Physics No. 2009 (2009), pp.1-21.
https://search.emarefa.net/detail/BIM-513912
American Medical Association (AMA)
Salgado, Gil& Vallejo-Rodríguez, José A.. The Meaning of Time and Covariant Superderivatives in Supermechanics. Advances in Mathematical Physics. 2009. Vol. 2009, no. 2009, pp.1-21.
https://search.emarefa.net/detail/BIM-513912
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-513912