01-345 Petko Al. Nikolov, Nikola P. Petrov

A Local Approach to Dimensional Reduction: I. General Formalism (395K, PS) Oct 1, 01

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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.

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