Quantization of p-branes, D-p-branes and M-branes

Killing spinors of space-time BPS configurations play an important role in quantization of theories with the fermionic worldvolume local symmetry. We show here how it works for the GS superstring, BST supermembrane and M-5-brane. We show that the non-linear generalization of the (2,0) d = 6 tensor supermultiplet action is the M-brane action in a Killing gauge. For D-p-branes the novel feature of quantization is that they can be quantized Lorentz covariantly, in particular, for D-0-brane a gauge exists where the action is covariant and free. We present a general condition on possible choice of gauges for the κ-symmetric branes. (orig.)