LIMITATIONS OF GAUGE INVARIANCE

GAUGE EQUIVALENT – BUT DIFFERENT
The most obvious difference is in the conservation of energy.
Written as H = kinetic energy + potential energy = T + V:
H
T
H' T'
V
constan t
t
;
V' 0
Evaluated with respective solutions: T = T' as expected.
This must be so because kinetic energy is measurable in the laboratory
and must be preserved by a gauge transformation.
HOWEVER: V V . THIS IS A FUNDAMENTAL DIFFERENCE.
In the original gauge, potential energy is converted into kinetic energy.
After the gauge transformation, kinetic energy grows as t 2 with no
source for this unlimited energy.
13