Field-Theoretic Variational Perturbation Theory

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

Field-Theoretic Variational Perturbation Theory

which has led to the most reliable results of strong-coupling

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,

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

found
precisely the value which I predicted in a seven-loop
calculation. For details, see

my
textbook on this subject

*Critical
Properties of phi^4 Theories*.

The relevant
papers are

Critical Exponents from Seven-Loop Strong-Coupling $\phi^4$-Theory in Three Dimensions

Strong-Coupling
phi^4-Theory in 4 -- epsilon Dimensions, and Critical Exponents

Critical
Exponents without beta-Function

Theory
and Satellite Experiment for Critical Exponent alpha of

lambda-Transition
in Superfluid Helium

Variational
Resummation of epsilon-Expansions of Critical Exponents

of
Nonlinear O(N)-Symmetric sigma-Model in 2+ epsilon Dimensions