Unfolded form of conformal equations in M dimensions and o(M+2)-modules

Details Unfolded form of conformal equations in M dimensions and o(M+2)-modules Unfolded form of conformal equations in M dimensions and o(M+2)-modules

2004-01-13

arxiv.org/abs/hep-th/0401086v4

Rev.Math.Phys. 18 (2006) 823-886

Physics

High Energy Physics

High Energy Physics - Theory

introduction extended, references added, the version to appear in Rev. Math. Phys

Scientific paper

A constructive procedure is proposed for formulation of linear differential equations invariant under global symmetry transformations forming a semi-simple Lie algebra f. Under certain conditions f-invariant systems of differential equations are shown to be associated with f-modules that are integrable with respect to some parabolic subalgebra of f. The suggested construction is motivated by the unfolded formulation of dynamical equations developed in the higher spin gauge theory and provides a starting point for generalization to the nonlinear case. It is applied to the conformal algebra o(M,2) to classify all linear conformally invariant differential equations in Minkowski space. Numerous examples of conformal equations are discussed from this perspective.

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