"Tom Ring" wrote in message
. net...
Frank wrote:
snip

Computation of the electric and magnetic fields in the vicinity of a
conductor involve manipulation of the "Vector magnetic potential";
as in:
http://en.wikipedia.org/wiki/Magnetic_vector_potential

Frank

Please no! Now he'll add gauge invariance to the mix!

You fool.

tom
K0TAR


here is the best description of art's equilibrium i have found:

Perturbative string theory may be used to show that massless particles can
only have spins 0, 1/2, 1, 3/2, 2. This conclusion follows from an analysis
of the energy of various harmonic oscillators included in the string that
contribute to the mass of the resulting particle. This conclusion
beautifully agrees with facts about gauge invariance that may be derived
using spacetime arguments.

If you consider any semirealistic physical system, it reduces to quantum
fields at long distances - fields that are able to create particles. Because
of the rotational symmetry, these particles may be classified according to
their spin. For spins equal to 0 or 1/2, one only creates states of positive
norms (think about the Klein-Gordon and Dirac fields). However, for spin 1
and higher, there are inevitably negative-norm states in the Hilbert space
created by the simplest version of these quantum fields. For example, the
time-like component of a 4-vector field creates states whose norm has the
opposite (negative) sign than the space-like components of the same field.
Such a decoupling implies an infinite amount of accidents that are
equivalent to a symmetry.