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Functional integration is one of the most powerful methods of
contempo rary theoretical physics, enabling us to simplify,
accelerate, and make clearer the process of the theoretician's
analytical work. Interest in this method and the endeavour to
master it creatively grows incessantly. This book presents a study
of the application of functional integration methods to a wide
range of contemporary theoretical physics problems. The concept of
a functional integral is introduced as a method of quantizing
finite-dimensional mechanical systems, as an alternative to
ordinary quantum mechanics. The problems of systems quantization
with constraints and the manifolds quantization are presented here
for the first time in a monograph. The application of the
functional integration methods to systems with an infinite number
of degrees of freedom allows one to uniquely introduce and
formulate the diagram perturbation theory in quantum field theory
and statistical physics. This approach is significantly simpler
than the widely accepted method using an operator approach."
Material particles, electrons, atoms, molecules, interact with one
another by means of electromagnetic forces. That is, these forces
are the cause of their being combined into condensed (liquid or
solid) states. In these condensed states, the motion of the
particles relative to one another proceeds in orderly fashion;
their individual properties as well as the electric and magnetic
dipole moments and the radiation and absorption spectra, ordinarily
vary little by comparison with their properties in the free state.
Exceptiotls are the special so-called collective states of
condensed media that are formed under phase transitions of the
second kind. The collective states of matter are characterized to a
high degree by the micro-ordering that arises as a result of the
interaction between the particles and which is broken down by
chaotic thermal motion under heating. Examples of such pheonomena
are the superfluidity of liquid helium, and the superconductivity
and ferromagnetism of metals, which exist only at temperatures
below the critical temperature. At low temperature states the
particles do not exhibit their individual characteristics and
conduct themselves as a single whole in many respects. They flow
along capillaries in ordered fashion and create an undamped current
in a conductor or a macroscopic magnetic moment. In this regard the
material acquires special properties that are not usually inherent
to it.
Material particles, electrons, atoms, molecules, interact with one
another by means of electromagnetic forces. That is, these forces
are the cause of their being combined into condensed (liquid or
solid) states. In these condensed states, the motion of the
particles relative to one another proceeds in orderly fashion;
their individual properties as well as the electric and magnetic
dipole moments and the radiation and absorption spectra, ordinarily
vary little by comparison with their properties in the free state.
Exceptiotls are the special so-called collective states of
condensed media that are formed under phase transitions of the
second kind. The collective states of matter are characterized to a
high degree by the micro-ordering that arises as a result of the
interaction between the particles and which is broken down by
chaotic thermal motion under heating. Examples of such pheonomena
are the superfluidity of liquid helium, and the superconductivity
and ferromagnetism of metals, which exist only at temperatures
below the critical temperature. At low temperature states the
particles do not exhibit their individual characteristics and
conduct themselves as a single whole in many respects. They flow
along capillaries in ordered fashion and create an undamped current
in a conductor or a macroscopic magnetic moment. In this regard the
material acquires special properties that are not usually inherent
to it.
Functional integration is one of the most powerful methods of
contempo rary theoretical physics, enabling us to simplify,
accelerate, and make clearer the process of the theoretician's
analytical work. Interest in this method and the endeavour to
master it creatively grows incessantly. This book presents a study
of the application of functional integration methods to a wide
range of contemporary theoretical physics problems. The concept of
a functional integral is introduced as a method of quantizing
finite-dimensional mechanical systems, as an alternative to
ordinary quantum mechanics. The problems of systems quantization
with constraints and the manifolds quantization are presented here
for the first time in a monograph. The application of the
functional integration methods to systems with an infinite number
of degrees of freedom allows one to uniquely introduce and
formulate the diagram perturbation theory in quantum field theory
and statistical physics. This approach is significantly simpler
than the widely accepted method using an operator approach."
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