  We combine the creation and annihilation operators of a scalar field in
Minkowski spacetime to obtain the generators of the SU(1,1). We show that the
transformation between Minkowski and Rindler vacua can be represented by
(pseudo)rotation in the space of the SU(1,1) group. The root of this fact
originates from the coordinate transformation between Minkowski and Rindler
manifolds that can also be represented as a (pseudo)rotation in SU(1,1) group.
The group structure reveals that an independent (pseudo)rotation in the group
space must exist which leads to a new vacuum state, independent Rindler vacuum.
The newly defined state shares many of the properties of the Rindler vacuum
and, in particular, the theorem of thermalization remains valid for it.
