email@example.com(Edward Green) writes: } } Speaking of gauge theories, I was about to ask the abysmaly dumb question } "what is gauge invariance?",
Why, invariance under a gauge transformation, of course. When thinking about what John writes
firstname.lastname@example.org (john baez) writes: > >A gauge theory is a theory where one of the fields is a "connection", >that lets you parallel transport something. I've explained these to you >a couple of times already. In general relativity the connection lets >you parallel transport tangent vectors ...
it could be helpful to make a mental connection to the meaning of "gauge" in the context of the tool used to set the width of railroad tracks. A 'standard measure' which is used in a more generalized context in electromagnetism, from whence it finds its way into other field theories.
You cannot transport something between rail systems that operate on a different gauge; similarly (even if it is a big conceptual leap with minimal analogous content) you can only make direct comparisons as long as you are working in a consistent gauge in a field theory. When terms like Coulomb Gauge and Lorentz Gauge were invented, the inventors knew more about railroads than we do today. Or so I claim: you won't find this in Jackson, but it provides a visualization of what it means for two formalisms to be physically equivalent even when the mathematics corresponds to some rotation in an abstract space.
-- James A. Carr <email@example.com> | "The half of knowledge is knowing http://www.scri.fsu.edu/~jac/ | where to find knowledge" - Anon. Supercomputer Computations Res. Inst. | Motto over the entrance to Dodd Florida State, Tallahassee FL 32306 | Hall, former library at FSCW.