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Topic: [Q:] Gauge and Grassmanian Schemes
Replies: 2   Last Post: Jun 16, 1996 4:14 PM

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Jim Carr

Posts: 42
Registered: 12/6/04
Re: [Q:] Gauge and Grassmanian Schemes
Posted: Jun 10, 1996 3:01 PM
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egreen@nyc.pipeline.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

baez@guitar.ucr.edu (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 <jac@scri.fsu.edu> | "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.







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