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A local approach to dimensional reduction: I. General formalism

✍ Scribed by Petko A. Nikolov; Nikola P. Petrov

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
136 KB
Volume
44
Category
Article
ISSN
0393-0440

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✦ Synopsis

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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