This theory
allows for the
arbitrarily precise calculations of strong-coupling
properties
of quantum field theories.
In particular, it enables one
to find critical exponents
near second-order phase transitions
in a simple way
without using renormalization group theory.
It makes essential use of the Wegner exponent
governing the approach to scaling
(which Pade and Pade-Borel methods are unable to do)
and determines it with high accuracy.
The theory
is based on an essential extension of the original
Feynman-Kleinert
Variational Approach
in two
steps.
First,
the Peierls inequality was abandoned in order to
deal with
expansions of any order. This turns divergent weak-coupling expansions
into convergent
strong-coupling expansions. The convergence is mostly exponentially
fast.
The details
are described in Chapter 5 of my textbook
Second,
a simple trick was found to accommodate
the anomalous
dimensions of quantum field theory. The result is
Field-Theoretic Variational
Perturbation Theory
which has led to the
most
reliable results of strong-coupling
properties
of field theories so far.
The
most-accurately measured strong-coupling property is the critical exponent
that governs the singularity of
the specific heat of superfluid helium,
which
was performed with great effort in amicrogravity environment
in
a satellite by
J. Lipa
and collaborators. This experiment
my
textbook on this subject
Critical
Properties of phi^4 Theories.
The relevant
papers are