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arXiv · 1801.08097

Bogoliubov transformation and the thermal operator representation in the real time formalism

Ashok Das·Atri Deshamukhya·Pushpa Kalauni·S. Panda
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Abstract

It has been shown earlier \cite{brandt,brandt1} that, in the mixed space, there is an unexpected simple relation between any finite temperature graph and its zero temperature counterpart through a multiplicative scalar operator (termed thermal operator) which carries the entire temperature dependence. This was shown to hold only in the imaginary time formalism and the closed time path ($σ=0$) of the real time formalism (as well as for its conjugate $σ=1$). We study the origin of this operator from the more fundamental Bogoliubov transformation which acts, in the momentum space, on the doubled space of fields in the real time formalisms \cite{takahashi,umezawa,pushpa}. We show how the ($2\times 2$) Bogoliubov transformation matrix naturally leads to the scalar thermal operator for $σ=0,1$ while it fails for any other value $0<σ<1$. This analysis also suggests that a generalized scalar thermal operator description, in the mixed space, is possible even for $0<σ<1$. We also show the existence of a scalar thermal operator relation in the momentum space.

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Ashok Das, Atri Deshamukhya, Pushpa Kalauni, S. Panda. 2018-02-05. Bogoliubov transformation and the thermal operator representation in the real time formalism. https://doi.org/10.1103/physrevd.97.045015

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