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Beginning with an introduction to the T-product approach in the
theory of a particle interacting with bosonic fields as applied,
for example, to the linearized polaron model, the book goes on to
deal with the equilibrium state investigation for the Fr lich
polaron model, the main objective being to derive Bogolubov's
inequality for the reduced free energy of the polaron. The third
chapter deals with some problems related to the non-equilibrium
polaron theory, including polaron kinetics. Finally, alternative
methods used in polaron theory are also presented and compared with
Bogolubov's method.
The majority of the "memorable" results of relativistic quantum
theory were obtained within the framework of the local quantum
field approach. The explanation of the basic principles of the
local theory and its mathematical structure has left its mark on
all modern activity in this area. Originally, the axiomatic
approach arose from attempts to give a mathematical meaning to the
quantum field theory of strong interactions (of Yukawa type). The
fields in such a theory are realized by operators in Hilbert space
with a positive Poincare-invariant scalar product. This "classical"
part of the axiomatic approach attained its modern form as far back
as the sixties. * It has retained its importance even to this day,
in spite of the fact that nowadays the main prospects for the
description of the electro-weak and strong interactions are in
connection with the theory of gauge fields. In fact, from the point
of view of the quark model, the theory of strong interactions of
Wightman type was obtained by restricting attention to just the
"physical" local operators (such as hadronic fields consisting of
''fundamental'' quark fields) acting in a Hilbert space of physical
states. In principle, there are enough such "physical" fields for a
description of hadronic physics, although this means that one must
reject the traditional local Lagrangian formalism. (The connection
is restored in the approximation of low-energy "phe nomenological"
Lagrangians."
The majority of the "memorable" results of relativistic quantum
theory were obtained within the framework of the local quantum
field approach. The explanation of the basic principles of the
local theory and its mathematical structure has left its mark on
all modern activity in this area. Originally, the axiomatic
approach arose from attempts to give a mathematical meaning to the
quantum field theory of strong interactions (of Yukawa type). The
fields in such a theory are realized by operators in Hilbert space
with a positive Poincare-invariant scalar product. This "classical"
part of the axiomatic approach attained its modern form as far back
as the sixties. * It has retained its importance even to this day,
in spite of the fact that nowadays the main prospects for the
description of the electro-weak and strong interactions are in
connection with the theory of gauge fields. In fact, from the point
of view of the quark model, the theory of strong interactions of
Wightman type was obtained by restricting attention to just the
"physical" local operators (such as hadronic fields consisting of
''fundamental'' quark fields) acting in a Hilbert space of physical
states. In principle, there are enough such "physical" fields for a
description of hadronic physics, although this means that one must
reject the traditional local Lagrangian formalism. (The connection
is restored in the approximation of low-energy "phe nomenological"
Lagrangians."
Introduction to Quantum Statistical Mechanics (Second Edition) may
be used as an advanced textbook by graduate students, even
ambitious undergraduates in physics. It is also suitable for non
experts in physics who wish to have an overview of some of the
classic and fundamental quantum models in the subject. The
explanation in the book is detailed enough to capture the interest
of the reader, and complete enough to provide the necessary
background material needed to dwell further into the subject and
explore the research literature.
Introduction to Quantum Statistical Mechanics (Second Edition) may
be used as an advanced textbook by graduate students, even
ambitious undergraduates in physics. It is also suitable for non
experts in physics who wish to have an overview of some of the
classic and fundamental quantum models in the subject. The
explanation in the book is detailed enough to capture the interest
of the reader, and complete enough to provide the necessary
background material needed to dwell further into the subject and
explore the research literature.
This volume looks at themes including: calculus of variations;
nonlinear mechanics and ergodic theory; and approximation and
asymptotics. The Krylov-Bogolubov method of averaging forms the
crux of the papers included in this volume, and numerous examples
of its applications are given. Bogolubov later returns to this
topic to prove the existence of quasi-periodic solutions of certain
mechanical systems whose number of degrees of freedom is more than
one.
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