  We show how generalized energy correlation functions can be used as a
powerful probe of jet substructure. These correlation functions are based on
the energies and pair-wise angles of particles within a jet, with (N+1)-point
correlators sensitive to N-prong substructure. Unlike many previous jet
substructure methods, these correlation functions do not require the explicit
identification of subjet regions. In addition, the correlation functions are
better probes of certain soft and collinear features that are masked by other
methods. We present three Monte Carlo case studies to illustrate the utility of
these observables: 2-point correlators for quark/gluon discrimination, 3-point
correlators for boosted W/Z/Higgs boson identification, and 4-point correlators
for boosted top quark identification. For quark/gluon discrimination, the
2-point correlator is particularly powerful, as can be understood via a
next-to-leading logarithmic calculation. For boosted 2-prong resonances the
benefit depends on the mass of the resonance.
