  We accurately treat the effect of the double and triple interactions of
two-level systems (TLS) in glasses onto the energy delocalization due to the
long-range interaction of TLS. Although this work qualitatively reproduces the
estimates of our previous work we believe that it is important because in this
paper the estimates are done with quantitative accuracy. This work can serve as
the important step towards the development of quantitative theory of many-body
delocalization due to the long-range interaction. Our study is compared with
the recent work by Bodea et al claiming that the interaction of TLS triples
leads to the energy delocalization. We cannot agree with the mentioned work
because as we show the interaction of TLS triples was overestimated there and
therefore the result for the TLS relaxation rate obtained there is invalid.
