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J. R. Klauder and B.-S. Skagerstam, Coherent States—Applications in Physics and Mathematical Physics (World Scientific, Singapore, 1985).
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The difference between the exact full quantum evolution of a system and its approximation is well known. For instance this aspect has been recently analyzed for a different coupled system by F. Cooper, J. Dawson, S. Habib and R. D. Ryne, Phys. Rev. E 57, 1489 (1998).
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A related attempt to evaluate fluctuations has been done by S. P. Kim, Phys. Rev. D 55, 7511 (1997).
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After the manuscript was completed we received the following private communication from R. Brout: “The work of R. Brout, F. Englert and E. Gunzig
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After the manuscript was completed we received the following private communication from R. Brout: “The work of R. Brout, F. Englert and E. Gunzig in 1, as well as the subsequent self-consistently driven approach of R. Brout, F. Englert and P. Spindel [Phys. Rev. Lett. 43, 417 (1979)] did not give full justice to the infrared sector of the fluctuations of the scalar field. Among other things, rescaling all the fields by the cosmological scale factor leads to surface terms which probably play a very important role in the infrared and hence their neglect results in a distortion of the true physics. The analysis of the fluctuations of the homogeneous mode in the present paper is a case in point. The physics is far richer than envisioned in our original work.”
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