Reply to comment on quantum oscillator in a non-self-interacting radiation field: Exact calculation of the partition function

In this Reply to the Comment by G. W. Ford, J. T. Lewis, and R. F. OConnell [Phys. Rev. A 37, 3609 (1988)] we refute the objections to our result on the partition function of a quantum oscillator interacting with the radiation field [Eq. (12) of D. P. L. Castrigiano and N. Kokiantonis, Phys. Rev. A 35, 4122 (1987)]. Furthermore, we show that the inclusion of the A2 term, which they propose, leads to a strong divergence in the limit of infinite cutoff frequency c. This divergence cannot be removed by the methods of renormalization applied so far. Therefore it does not appear that the inclusion of the A2 term would reproduce the result of G. W. Ford, J. T. Lewis, and R. F. OConnell [Phys. Rev. Lett. 55, 2273 (1985)] obtained earlier. Moreover, this fact constitutes an additional objection to that result [see p. 4124 of D. P. L. Castrigiano and N. Kokiantonis, Phys. Rev. A 35, 4122 (1987)] where only analogous methods of renormalization are applied.