title: 
Geometric approach to BRSTsymmetry and ZNgeneralization of superconnection 

publication: 

volumeissue:  13  Supplement  
pages:  9  20  
ISSN: 
14029251  
DOI: 
doi:10.2991/jnmp.2006.13.s.2 (how to use a DOI)  
author(s): 
V ABRAMOV, O LIIVAPUU 

publication date: 
August 2006 

abstract: 
We propose a geometric approach to the BRSTsymmetries of the Lagrangian of a
topological quantum field theory on a four dimensional manifold based on the formalism of superconnections. Making use of a graded qdifferential algebra, where q is a
primitive Nth root of unity, we also propose a notion of ZN connection which is a
generalization of a superconnection. In our approach the Lagrangian of a topological
field theory is presented as the value of the curvature of a superconnection evaluated
at an appropriate section of a vector bundle. Since this value of the curvature satisfies
the Bianchi identity and representing the Bianchi identity in this case in the form of
an operator applied to the mentioned above value of the curvature we obtain an operator which gives zero when applied to the Lagrangian. We show that this operator
generates the BRSTtransformations of the fields of a topological field theory on a
four dimensional manifold.


copyright: 
© The authors.
This article is distributed under the terms of the Creative Commons Attribution License 4.0, which permits noncommercial use, distribution and reproduction in any medium, provided the original work is properly cited. See for details: https://creativecommons.org/licenses/bync/4.0/ 

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