The Meaning of Time and Covariant Superderivatives in Supermechanics
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 an...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2009-01-01
|
| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2009/987524 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832550795588927488 |
|---|---|
| author | Gil Salgado José A. Vallejo-Rodríguez |
| author_facet | Gil Salgado José A. Vallejo-Rodríguez |
| author_sort | Gil Salgado |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-8bb4e37b3679422d8e2c3d091af87ef3 |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2009-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-8bb4e37b3679422d8e2c3d091af87ef32025-02-03T06:05:47ZengWileyAdvances in Mathematical Physics1687-91201687-91392009-01-01200910.1155/2009/987524987524The Meaning of Time and Covariant Superderivatives in SupermechanicsGil Salgado0José A. Vallejo-Rodríguez1Departamento de Matemáticas, Facultad de Ciencias, Universidad Autónoma de San Luis Potosí, 78290, MexicoDepartamento de Matemáticas, Facultad de Ciencias, Universidad Autónoma de San Luis Potosí, 78290, MexicoWe 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.http://dx.doi.org/10.1155/2009/987524 |
| spellingShingle | Gil Salgado José A. Vallejo-Rodríguez The Meaning of Time and Covariant Superderivatives in Supermechanics Advances in Mathematical Physics |
| title | The Meaning of Time and Covariant Superderivatives in Supermechanics |
| title_full | The Meaning of Time and Covariant Superderivatives in Supermechanics |
| title_fullStr | The Meaning of Time and Covariant Superderivatives in Supermechanics |
| title_full_unstemmed | The Meaning of Time and Covariant Superderivatives in Supermechanics |
| title_short | The Meaning of Time and Covariant Superderivatives in Supermechanics |
| title_sort | meaning of time and covariant superderivatives in supermechanics |
| url | http://dx.doi.org/10.1155/2009/987524 |
| work_keys_str_mv | AT gilsalgado themeaningoftimeandcovariantsuperderivativesinsupermechanics AT joseavallejorodriguez themeaningoftimeandcovariantsuperderivativesinsupermechanics AT gilsalgado meaningoftimeandcovariantsuperderivativesinsupermechanics AT joseavallejorodriguez meaningoftimeandcovariantsuperderivativesinsupermechanics |