  In this paper we calculated the n-point hard-thermal-loop (HTL) vertex
functions in QCD/QED for n= 2, 3 and 4 in the physical representation in the
real time formalism (RTF). The result showed that the n-point HTL vertex
functions can be classified into two groups, a) those with odd numbers of
external retarded indices, and b) the others with even numbers of external
retarded indices. The n-point HTL vertex functions with one retarded index,
which obviously belong to the first group a), are nothing but the HTL vertex
functions that appear in the imaginary time formalism (ITF), and vise versa.
All the HTL vertex functions belonging to the first group a) are of $O(g^2T^2)$
, and satisfy among them the simple QED-type Ward-Takahashi identities, as in
the ITF. Those vertex functions belonging to the second group b) never appear
in the ITF, namely their existence is characteristic of the RTF, and their
HTL's have the high temperature behavior of $O(g^2T^3)$, one-power of T higher
than usual. Despite this difference we could verify that those HTL vertex
functions belonging to the second group b) also satisfy among themselves the
QED-type Ward-Takahashi identities, thus guaranteeing the gauge invariance of
the HTL's in the real time thermal QCD/QED.
