with the corresponding quantum field theories.
v) Several tentatives to prove the existence of global solutions to the M-D equations, with
other techniques than those originally employed in [14], have been published; cf. [16] for an
interesting, but incomplete, approach based on Sobolev techniques and [3] for an attempt
based on obtaining local solutions in low regularity energy spaces.
vi) In lower dimensions (1 + 1 dimensions) it was proved in [5] that the Cauchy problem
for the M-D equations has global solutions even for large initial data.
Acknowledgement: The authors want to thank Daniel Sternheimer for several interest-
ing discussions during the long period of elaboration of our work and a very careful reading
of the present manuscript.
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