Quantized null p-branes in light-cone gauge have physical Hilbert spaces split into p+1 classes of standing-wave states.
A New Approach to the Classical and Quantum Dynamics of Branes
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abstract
It is shown that the Dirac-nambu-Goto brane can be described as a point particle in an infinite dimensional brane space with a particular metric. This suggests a generalization to brane spaces with arbitrary metric, including the "flat" metric. Then quantization of such a system is straightforward: it is just like quantization of a bunch of non interacting particles. This leads us to a system of a continuous set of scalar fields. For a particular choice of the metric in the space of fields we find that the classical Dirac-Nambu-Goto brane theory arises as an effective theory of such an underlying quantum field theory. Quantization of branes is important for the brane world scenarios, and thus for "quantum gravity".
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Towards Quantizing Null p-branes: Light-Cone Gauge Analysis and Physical Hilbert Space
Quantized null p-branes in light-cone gauge have physical Hilbert spaces split into p+1 classes of standing-wave states.