TY - JOUR
A2 - Cariñena, José F.
AU - Salgado, Gil
AU - Vallejo-Rodríguez, José A.
PY - 2009
DA - 2009/07/02
TI - The Meaning of Time and Covariant Superderivatives in Supermechanics
SP - 987524
VL - 2009
AB - We present a review of the basics of supermanifold theory(in the sense of Berezin-Kostant-Leites-Manin) from a physicist'spoint of view. By considering a detailed example of what does it meanthe expression “to integrate an ordinary superdifferential equation”we show how the appearance of anticommuting parameters playing therole of time is very natural in this context. We conclude that indynamical 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 weanalyze from a group-theoretic point of view what is the meaning of the usualcovariant superderivatives, relating them to a change in the underlying group law. This result is extended to the case of N-supersymmetry.
SN - 1687-9120
UR - https://doi.org/10.1155/2009/987524
DO - 10.1155/2009/987524
JF - Advances in Mathematical Physics
PB - Hindawi Publishing Corporation
KW -
ER -