From: sarfatti@well.sf.ca.us (Jack Sarfatti)
Subject: Feynman 39. QED & renormalization part I
Organization: Whole Earth 'Lectronic Link
Date: Sun, 20 Dec 1992 19:58:44 GMT


In order to properly evaluate recent developments in quantum gravity and
also, for example, in Puthoff's attempt to tap zero-point energy , possibly
for rocket propulsion in the not too distant future, it is important to
understand the background of standard work. The most visualizable is that
of Feynman - though it is limited to perturbation theory it is the correct
conceptual framework. It is clear that quantum gravity requires
non-perturbative methods.

Feynman 39 QED & renormalization Part I

"... considerable simplification in writing down matrix elements ....
Electrodynamics is modified by altering the interaction of electrons at
short distances ... All matrix elements are now finite, with the exception
of those relating to problems of vacuum polarization.  The latter are
evaluated in a manner suggested by Pauli and Bethe, which gives finite
results for these matrices also.  The only effects sensitive to the
modification are changes in mass and charge of the electrons. Such changes
could not be directly observed. Phenomena directly observable are
insensitive to the details of the modification .... For such phenomena, a
limit can be taken as the range of the modification goes to zero.....

The simplification results from an emphasis on the over-all space-time view
... from a study of the solution of the equations of electrodynamics.  The
relation of this to the more conventional Hamiltonian point of view is
discussed.  It would be very difficult to make the modification ,,,, if one
insisted on having the equations in Hamiltonian form."

Feynman is saying that the historical point of view is superior to the "be
here now" point of view.

"... previous methods unnecessarily separated into individual terms
processes that were closely related physically. For example, in the
exchange of a quantum between two electrons there were terms depending on
which electron emitted and which absorbed the quantum.  Yet, in the virtual
states considered, timing relations are not significant.  Only the order of
operators in the matrix must be maintained. ...

A modification in interaction between charges is next made, and it is shown
that the self-energy is made convergent and corresponds to a correction in
the electron mass.  After the mass correction is made, other real processes
are finite and insensitive to the 'width' of the cut-off in the
interaction. ... Unfortunately, the modification proposed is not completely
satisfactory theoretically (it leads to some difficulties in conservation
of energy).  It does, however, seem consistent and satisfactory to define
the matrix element for all real processes as the limit of that computed
here as the cut-off width goes to zero.  A similar technique .... applied
to problems of vacuum polarization (resulting in a renormalization of
charge) ...  a strict physical basis for the rules of convergence is not
known.

Briefly the genesis of this theory was this.  The conventional
electrodynamics was expressed in the Lagrangian form of quantum mechanics
... The motion of the field oscillators could be integrated out ... the
result being an expression of the delayed interaction of the particles.
Next the modification of the delta-function interaction could be made
directly from the analogy to the classical case .... the Lagrangian method
.. was then modified in accordance with the requirements of the Dirac
equation and the phenomenon of pair creation .. Finally for practical
calculations the expressions were developed in a power series in e^2/hc ...
each term in the series had a simple physical interpretation.

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