This book formulates a unified approach to the description of many-particle systems combining the methods of statistical physics and quantum field theory. The benefits of such an approach are in the description of phase transitions during the formation of new spatially inhomogeneous phases, as well in describing quasi-equilibrium systems with spatially inhomogeneous particle distributions (for example, self-gravitating systems) and metastable states. The validity of the methods used in the statistical description of many-particle systems and models (theory of phase transitions included) is discussed and compared. The idea of using the quantum field theory approach and related topics (path integration, saddle-point and stationary-phase methods, Hubbard-Stratonovich transformation, mean-field theory, and functional integrals) is described in detail to facilitate further understanding and explore more applications. To some extent, the book could be treated as a brief encyclopedia of methods applicable to the statistical description of spatially inhomogeneous equilibrium and metastable particle distributions. Additionally, the general approach is not only formulated, but also applied to solve various practically important problems (gravitating gas, Coulomb-like systems, dusty plasmas, thermodynamics of cellular structures, non-uniform dynamics of gravitating systems, etc.).
This book formulates a unified approach to the description of many-particle systems combining the methods of statistical physics and quantum field theory. The benefits of such an approach are in the description of phase transitions during the formation of new spatially inhomogeneous phases, as well in describing quasi-equilibrium systems with spatially inhomogeneous particle distributions (for example, self-gravitating systems) and metastable states. The validity of the methods used in the statistical description of many-particle systems and models (theory of phase transitions included) is discussed and compared. The idea of using the quantum field theory approach and related topics (path integration, saddle-point and stationary-phase methods, Hubbard-Stratonovich transformation, mean-field theory, and functional integrals) is described in detail to facilitate further understanding and explore more applications. To some extent, the book could be treated as a brief encyclopedia of methods applicable to the statistical description of spatially inhomogeneous equilibrium and metastable particle distributions. Additionally, the general approach is not only formulated, but also applied to solve various practically important problems (gravitating gas, Coulomb-like systems, dusty plasmas, thermodynamics of cellular structures, non-uniform dynamics of gravitating systems, etc.).
Foreword; Introduction; Statistical Physics of Interacting Particle Systems; Statistical Description of Phase Transitions; Path Integration and the Field Theory; Peculiarity of Calculation of Some Models; Statistical Description of the Condensed Matter; Inhomogeneous Distribution in Systems of Interacting Particles; Cellular Structures in the Condensed Matter; Statistical Description of Nonequilibrium Interacting Systems; Conclusions; Bibliography;
Bohdan Lev, Head of the Department of Synergetics of the Bogolyubov
Institute of Theoretical Physics of the National Academy of
Sciences of Ukraine (NAS of Ukraine), Corresponding Member of the
NAS of Ukraine, author of over 200 publications, including three
books: Some issues of condensed matter physics (2008) Structures in
liquid crystal colloids (2015) and Liquid crystal colloids. The
same aspects of the theory (2018).
Anatoly Zagorodny, Director of the Bogolyubov Institute of
Theoretical Physics of the National Academy of Sciences of Ukraine,
Vice President of the National Academy of Sciences of Ukraine,
Academician of the National Academy of Sciences of Ukraine, author
of over 200 scientific papers, including three books: Statistical
Theory of Plasma Molecular Systems (1990), Introduction to Plasma
Physics (2014), Introduction to the kinetic theory of plasma
(2015).
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