eFTC-020701

Statistical Field Dynamics
30 July 2002

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Abstract

In this work, we build on the structural foundations of the Thermo Field Dynamics (TFD) and Non Equilibrium Thermo Field Dynamics (NETFD) formalisms of the late Prof. H. Umezawa, as well as the author’s own Microcanonical Field Dynamics (MFD) formalism for fixed energy systems near thermodynamical equilibrium, and develop a general formalism unifying fully Quantum Statistical Mechanics (QSM) with Quantum Field Theory (QFT) in any ensemble. The Feynman diagrams method of perturbation theory is fully implementable for systems in arbitrary statistical equilibrium in ways completely analogous to the thermal case, and so are the concepts of renormalization and renormalization group. In the context of NETFD, we further show how to derive the general Master equation for transition probabilities using the loop expansion. For certain types of interactions such as the reservoir model, we obtain the expected Markovian behavior. Physical applications are to be found in so-called small (non-extensive) systems such as nuclear matter or systems with long range interactions such as gravity (e.g. black holes, strings, p-branes) for which no thermodynamical limit exists. The formalism is also useful in statistical fluctuations calculations and phase transitions at finite volume (e.g. nuclear fragmentation and multifragmentation as well as gravitational collapse). We shall call this formalism Statistical Field Dynamics (SFD).

Copyright © 2002 Yvan Leblanc. All rights reserved

PACS: 05.30.Ch, 03.70.+k, 11.10.Gh

Cite as: Leblanc, Y., "Statistical Field Dynamics", manuscript no. eFTC-020701 (2002). http://www.efieldtheory.com/abs/?eFTC-020701; doi:10.13140/RG.2.1.4800.2409.