Harmonic resolution as a holographic quantum number

The Bekenstein bound takes the holographic principle into the realm of flat space, promising new insights on the relation of non-gravitational physics to quantum gravity. This makes it important to obtain a precise formulation of the bound. Conventionally, one specifies two macroscopic quantities, mass and spatial width, which cannot be simultaneously diagonalized. Thus, the counting of compatible states is not sharply defined. The resolution of this and other formal difficulties leads naturally to a definition in terms of discretized light-cone quantization. In this form, the area difference specified in the covariant bound converts to a single quantum number, the harmonic resolution K. The Bekenstein bound then states that the Fock space sector with K units of longitudinal momentum contains no more than exp(2 pi^2 K) independent discrete states. This conjecture can be tested unambiguously for a given Lagrangian, and it appears to hold true for realistic field theories, including models arising from string compactifications. For large K, it makes contact with more conventional but less well-defined formulations.