A reformulation of the fluctuation-dissipation theorem of Callen and Welton [Phys. Rev. 83, 34 (1951)] is presented in such a manner that the basic idea of Feynman Vernon [Ann. Phys. (N.Y.) 24, 118 (1963)] and Caldeira and Leggett [Ann. Phys. (N.Y.) 149, 374 (1983); Phys. Rev. Lett. 46, 211 (1981)] of using an infinite number of oscillators to-simulate the dissipative medium is realized manifestly without actually introducing oscillators. If one assumes the existence of a well defined dissipative coefficient R(omega), which depends little on the temperature in the energy region we are interested in, the spontaneous and induced emissions as well as induced absorption of these effective oscillators,with a correct Bose distribution automatically appear. Combined with a dispersion relation, we reproduce the tunneling formula in the presence of dissipation at a finite temperature without referring to an explicit model Lagrangian. The fluctuation-dissipation theorem of Callen and Welton is also generalized to the fermionic dissipation (or fluctuation), which allows a transparent physical interpretation in terms of second-quantized fermionic oscillators. This fermionic version of the fluctuation-dissipation theorem may become relevant in the analyses of, for example, fermion radiation from a black hole and also supersymmetry in the early Universe. [S1063-651X(98)04812-0]. [References: 15]
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