Conformal fields: a class of representations of Vect(N)

Abstract

$Vect(N)$, the algebra of vector fields in $N$ dimensions, is studied. Some aspects of local differential geometry are formulated as $Vect(N)$ representation theory. There is a new class of modules, {\it conformal fields}, whose restrictions to the subalgebra $sl(N+1)\subset Vect(N)$ are finite-dimensional $sl(N+1)$ representations. In this regard they are simpler than tensor fields. Fock modules are also constructed. Infinities, which are unremovable even by normal ordering, arise unless bosonic and fermionic degrees of freedom match.

16 pages

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