Energy operator

Abstract: Teager's energy operators are defined in both the continuous and discrete domains and are very useful tools for analyzing single component signals from an energy point of view. A number of important properties of these operators are shown that make it possible to determine the energy functions of quite complicated functions, provided these functions can be expressed as products of simpler functions, this operation of function multiplication being typical of a modulation process. Some of the eigenfunction properties of the energy operator that illustrate the special role of the trigonometric, Gaussian, and single soliton functions are also given. >

Abstract: We argue that every CFT contains light-ray operators labeled by a continuous spin J. When J is a positive integer, light-ray operators become integrals of local operators over a null line. However for non-integer J , light-ray operators are genuinely nonlocal and give the analytic continuation of CFT data in spin described by Caron-Huot. A key role in our construction is played by a novel set of intrinsically Lorentzian integral transforms that generalize the shadow transform. Matrix elements of light-ray operators can be computed via the integral of a double-commutator against a conformal block. This gives a simple derivation of Caron-Huot’s Lorentzian OPE inversion formula and lets us generalize it to arbitrary four-point functions. Furthermore, we show that light-ray operators enter the Regge limit of CFT correlators, and generalize conformal Regge theory to arbitrary four-point functions. The average null energy operator is an important example of a light-ray operator. Using our construction, we find a new proof of the average null energy condition (ANEC), and furthermore generalize the ANEC to continuous spin.