Isolating vacuum amplitudes in quantum field calculations at finite temperature |
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Institution: | 1. Service de Physique Théorique, CEA/DSM/SPhT, 91191 Gif-sur-Yvette Cedex, France;2. Institut für Theoretische Physik, Technische Univeristät Wien, Wiedner Hauptstrasse 8-10/136, A-1040 Wien, Austria;1. Department of Physics, Vidyasagar Evening College, 39 Sankar Ghosh Lane, Kolkata 700006, India;2. Department of Physics, University of Calcutta, 92 Acharya Prafulla Chandra Road, Kolkata 700009, India;1. Dipartimento di Fisica e Astronomia, Università di Bologna, via Irnerio 46, I-40126 Bologna, Italy;2. INFN, Sezione di Bologna, via Irnerio 46, I-40126 Bologna, Italy |
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Abstract: | In calculating Feynman diagrams at finite temperature, it is sometimes convenient to isolate subdiagrams which do not depend explicitly on the temperature. We show that, in the imaginary time formalism, such a separation can be achieved easily by exploiting a simple method, due to Gaudin, to perform the sum over the Matsubara frequencies. In order to manipulate freely contributions which may be individually singular, a regularization has to be introduced. We show that, in some cases, it is possible to choose this regularization in such a way that the isolated subdiagrams can be identified with analytical continuations of vacuum n-point functions. However, at least with the regularization used in this paper, this simple analytical structure does not hold for arbitrary diagrams, as revealed by counter-examples. As an aside illustration of Gaudin's method, we use it to prove the main part of a recent conjecture for a relation, in the imaginary time formalism, between the expressions of a Feynman diagram at zero and finite temperature. |
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