  A many-body theory of paramagnetic Kondo insulators is described, focusing
specifically on single-particle dynamics, scattering rates, d.c. transport and
optical conductivities. This is achieved by development of a non-perturbative
local moment approach to the symmetric periodic Anderson model within the
framework of dynamical mean-field theory. Our natural focus is the strong
coupling, Kondo lattice regime; in particular the resultant `universal' scaling
behaviour in terms of the single, exponentially small low-energy scale
characteristic of the problem. Dynamics/transport on all relevant ($\omega, T$)
scales are considered, from the gapped/activated behaviour characteristic of
the low-temperature insulator through to explicit connection to single-impurity
physics at high $\omega$ and/or $T$; and for optical conductivities emphasis is
given to the nature of the optical gap, the temperature scale responsible for
its destruction, and the consequent clear distinction between indirect and
direct gap scales. Using scaling, explicit comparison is also made to
experimental results for d.c. transport and optical conductivites of
Ce_3Bi_4Pt_3, SmB_6 and YbB_{12}. Good agreement is found, even quantitatively;
and a mutually consistent picture of transport and optics results.
