  In this brief report we discuss the action functional of a particle with
damping, showing that it can be obtained from the dissipative equation of
motion through a modification which makes the new dissipative equation
invariant for time reversal symmetry. This action functional is exactly the
effective action of Caldeira-Leggett model but, in our approach, it is derived
without the assumption that the particle is weakly coupled to a bath of
infinite harmonic oscillators.
