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Abstract:
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In classical field theory, the ordinary potential V
is an energy density for that state in which the field assumes
the value ¢. In quantum field theory, the effective potential
is the expectation value of the energy density for which the
expectation value of the field is ¢o. As a result, if V has
several local minima, it is only the absolute minimum that
corresponds to the true ground state of the theory.
Perturbation theory remains to this day the main
analytical tool in the study of Quantum Field Theory. However,
since perturbation theory is unable to uncover the whole rich
structure of Quantum Field Theory, it is desirable to have some
method which, on one hand, must go beyond both perturbation
theory and classical approximation in the points where these
fail, and at that time, be sufficiently simple that analytical
calculations could be performed in its framework During the last decade a nonperturbative variational
method called Gaussian effective potential, has been discussed
widely together with several applications. This concept was
described as a means of formalizing our intuitive understanding
of zero-point fluctuation effects in quantum mechanics in
a way that carries over directly to field theory. |