- 01-345 Petko Al. Nikolov, Nikola P. Petrov
- A Local Approach to Dimensional Reduction:
I. General Formalism
Oct 1, 01
(auto. generated ps),
of related papers
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
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.