Re: gauge invariance

["John S. Denker" <jsd@MONMOUTH.COM>]

At 05:01 PM 3/1/01 -0500, Ludwik Kowalski wrote:
> Can somebody explain the "gauge invariance"?

Definition: In this context a gauge is something which, when added to a
field, produces no observable physical consequences.

> why is it called that way?

Here is my guess.  No guarantees.  The word "gauge" has a quite a cluster
of meanings, mostly clustered around the notion of "a way of measuring".
  http://www.m-w.com/cgi-bin/dictionary?va=gauge

1) You may be familiar with the notion of "gauge" pressure (PSIG) as
opposed to "absolute" pressure (PSIA).  This is an inexact gauge
invariance, but for many pneumatic applications it is a useful approximate
invariance.

2) The electrostatic potential is an exact gauge invariance.   You have to
measure the potential relative to SOME reference, and it doesn't matter
what.  Alice can choose one reference, Bob can choose another, and Charlie
can choose another.  They will assign different numbers to the field, but
the laws of physics will be unaffected (as long as the choice is made
consistently).

3) The magnetic "vector potential" is another exact gauge invariance.

4) Potential energy is another exact gauge invariance.

> It probably has somethinbg to do with symmetry and energy but I am not sure.

-- The word "invariance" and the word "symmetry" express the same idea.
-- Potential energy is just one example of the broader notion of gauge
invariance.

> Is it a new concept or a new term for something that used to have
> a different name?

The idea has been explicit since 1918 if not longer.
  http://www.theophys.kth.se/~gli/SYM/sym_history.html