**Stephen P. King** (*stephenk1@home.com*)

*Sat, 13 Mar 1999 21:50:16 -0500*

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Here we go!

http://www.phys.ndsu.nodak.edu/mrm8/titles.htm

Michael J. Martin, University of Missouri

Reformulating Weyl's Unified Field Theory of 1919

In 1918-19, Hermann Weyl introduced the first classical unified

field theory, a theory that united electromagnetism and general

relativity into one geometrical framework. This theory, the forerunner

of modern gauge theory, involved transforming the metric 2-tensor with a

"scale factor" that, in turn, transformed the line element, causing

lengths of parallel transported vectors, as well as their orientations,

to change. This length dependence was later dismissed, and reformulated

by London and Fock as wave function phase dependence. We attempt another

reformulation, whereby the volume element varies on parallel transport

(volume instead of length) unless it is transformed into a tensor

density. This transformation introduces a gauge potential, the

contracted Christoffel symbol, which maintains invariance under

covariant differentiation.

The electromagnetic potential, in pure gauge form, is shown to be

equivalent to a constant multiple of the contracted Christoffel symbol.

The gravitational field is introduced into wave mechanics via the

contracted Christoffel symbol, which appears as an integrable phase

factor. The contracted Christoffel symbol and the electromagnetic

4-potential are related via a simple gauge transformation under this

program.

Density Transformations in a Gauge Unification of Gravity and

Electromagnetism

The Lagrangian which describes an electron wavefunction in QED

remains invariant under local phase transformations through a gauge

transformation of the electromagnetic 4-potential, which is the gauge

connection appearing in the QED covariant derivative. We postulate that

similarly, the Lagrangian which describes the electron wavefunction in

both an electromagnetic and gravitational field remains invariant under

local phase transformations of the wave function density, via the

introduction of the contracted Christoffel symbol as gauge connection in

the covariant derivative. The resulting transformations, of the QED

Lagrangian density, are explored. The quanta of the gravitational field

would appear to be both massless and of infinite range, as the

transformations are nearly identical to U(1). We explore the case of

wave function --> wave function density, and wave function

density-->wave function density, where a density is defi.....

http://smatc.fcc.cc.md.us/staff/mjm/index.htm

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**Next message:**Stephen P. King: "[time 16] Re: God"**Previous message:**Stephen P. King: "[time 14] Re: Gravitational Aharonov-Bohm Effect"

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