LIGHTFRONT HOLOGRAPHY AND AREA DENSITY OF ENTROPY ASSOCIATED WITH LOCALIZATION ON WEDGE-HORIZONS

Abstract

It is shown that a suitably formulated algebraic lightfront holography (LFH), in which the lightfront is viewed as the linear extension of the upper causal horizon of a wedge region, is capable of overcoming the shortcomings of the old lightfront quantization. The absence of transverse vacuum fluctuations which this formalism reveals is responsible for an area (edge of the wedge) — rearrangement of degrees of freedom which in turn leads to the notion of area density of entropy for a "split localization." This area proportionality of horizon associated entropy has to be compared to the volume dependence of ordinary heat bath entropy. The desired limit, in which the split distance vanishes and the localization on the horizon becomes sharp, can at most yield a relative area density which measures the ratio of area densities for different quantum matter. In order to obtain a normalized area density one needs a (yet unknown) analog of a second fundamental law of thermodynamics in case the thermalization is caused by vacuum fluctuation through localization on causal horizons. This is similar to the role of the classical Gibbs form of that law which relates Bekenstein's classical area formula with the Hawking quantum mechanism for thermalization from black holes.