Petko Al. Nikolov, Nikola P. Petrov
A Local Approach to Dimensional Reduction: 
I. General Formalism
(395K, PS)

ABSTRACT.  We present a formalism for dimensional reduction based on
the local properties of invariant cross-sections (``fields'') 
and differential operators.
This formalism does not need an ansatz for the invariant fields 
and is convenient when the reducing group 
is non-compact. 
In the approach presented here, splittings of some exact sequences 
of vector bundles play a key role. 
In the case of invariant fields and differential operators, 
the invariance property leads to an explicit splitting 
of the corresponding sequences, 
i.e., to the reduced field/operator. 
There are also situations when 
the splittings do not come 
from invariance with respect to a group action 
but from some other conditions, 
which leads to a ``non-canonical'' reduction. 
In a special case, studied in detail 
in the second part of this article, 
this method provides an algorithm 
for construction of conformally invariant 
fields and differential operators in Minkowski space.