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What is a gauge? A lively discussion by experts on Face-book

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Sudhir Raniwala
Yesterday at 10:16 ·
 

A student asked a question that I do not have an answer to, and need an answer that satisfies me. I introduced Coulomb gauge, and was asked 'What is a gauge'. Sure, I can talk about gauge transformations, gauge conditions, choice of gauge fixing and the potential and all that. The question is more fundamental 'what is gauge'?

 

 
 
 
Raman Khurana Never got a satisfactory answer to this, I will follow-up what others have to say..
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Gautam Menon
Gautam Menon A way of defining electromagnetic potentials that removes the ambiguity which arises from the fact that these potentials are not unique and can be redefined to yield the same physical B,E fields?
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Sudhir Raniwala
Sudhir Raniwala Sure. That is a gauge transformation, as against what is a 'gauge'.
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Gautam Menon
Gautam Menon Sudhir Raniwala I understood the gauge to be the precise choice of the transformation.
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Sudhir Raniwala
Sudhir Raniwala Gautam Menon Please see my original post....it says as much '...choice of gauge fixing and the potential and all that'. I know what is a book --- I can see it, and make a picture also. I know what is Electric field, thanks to the idea of flux and representation in terms of lines of force which help me understand the abstract quantity E. The question remains --- what is gauge?
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Sudhir Raniwala
Sudhir Raniwala Gautam Menon In other words, can we define gauge without using 'transformations'.
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Gautam Menon
Gautam Menon Ah, I understand what you are asking. In my opinion, no.
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Gautam Menon
Gautam Menon Much as saying we are free to decide the zero of any potential, without affecting the physics, This does not have physical content - at least that is the way I understand it.
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Sudhir Raniwala
Sudhir Raniwala Here is an attempt: Vector (scalar) potential can be defined only by making a 'choice', else it does not have a meaning. That choice is the gauge. It is a little like the 'scale' --- defining a meter of length is a 'choice' --- we fix the scale when we define a meter. An absolute definition of potential fixes something that may be called a gauge. (Frankly, I had never thought about it as explicitly).
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Gautam Menon
Gautam Menon Seems OK to me, except maybe the line "It is a little like the 'scale' --- defining a meter of length is a 'choice' --- we fix the scale when we define a meter.' I've seen this analogy used but never really understood why a choice of units should be equivalent to a gauge choice. But maybe someone who has thought about these things more than I have will be able to comment.
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Sudhir Raniwala
Sudhir Raniwala It is not just a choice of units....it is what (physical) length is to be termed as one meter.
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Maripat Abu Adil
Maripat Abu Adil I agree with Gautams comments and I agree with Sudhir's final assessment and I also feel that therein lies the answer to the query.
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Sudhir Raniwala
Sudhir Raniwala Maripat Abu Adil Not so early.....there are other issues....the idea is more complex. But I still need to work on what I have to teach today :-)
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Ashok Kapoor
Write a reply...
Nitin Gupta
Nitin Gupta What about this? Gauge is formally defined as "determining the amount of something".. Since there is an ambiguity in potentials we need a way to determine quantities uniquely...that way is Columb/Lorenz in case of EM theory and and since it allows us to give unique measurements we call it a gauge.
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Pankaj Sharan
 
Pankaj Sharan

Pankaj Sharan The following (from notes for a lecture I was preparing) might help explain the context: The first gauge theory was Hermann Weyl's extension of Einstein's general theory of relativity with a parallel transport that can change the scale or 'gauge' of lengths of the transported vector. About this one can read in P. G. Bergman's book on Relativity. The Hamiltonian formulation of electrodynamics, and in particular, the replacement of \(\vec{p}\) by \(\vec{p}-e\vec{A}/c \) was given by Larmor in his book "Aether and Matter", Cambridge (1900). [quoted by Pauli in ``General Principles of Quantum Mechanics" , Section 4. (Tr. by P. Achuthan and K. Venkatesan of 1958 German edition) Allied, New Delhi 1980.]  In quantum mechanics the `canonical momentum' \(\vec{p}-e\vec{A}/c\) becomes \(-i\hbar[\nabla-ie\vec{A}/(\hbar c)]\). The gauge invariance of the Schrodinger theory under \(\vec{A}\to \vec{A}+\nabla f\) and \(\phi\to \phi-(e/c)\frac{\partial f}{\partial t} \) when \(\Psi\) is changed by a phase was first given by V. Fock (1927). The analogy of this group of transformations to the Weyl theory on gravitation and electricity was pointed out by F. London (1927). The connection of this group to charge conservation was pointed out by Weyl while writing variational principle for the wave equation. [See Pauli as above.]














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Sudhir Raniwala
Sudhir Raniwala Merci ! I do not have the capability to communicate this to the students in any way that there be an absorption. The bandwidths (and the peak) of students in different universities is very different.
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Pankaj Sharan
Pankaj Sharan Well, the lecture was meant for PhD students. Most jargon words in physics have historical roots. As for the word 'gauge', the above line of history should be told, even if briefly. Connecting its use somehow to the the dictionary meaning of gauge is not fair to the people who contributed so much to our understanding. Try explaining 'strangeness', or 'charm' not by history, but by dictionary meanings!
 
 
 
 
 
Sudhir Raniwala
Sudhir Raniwala Pankaj Sharan Frankly, until you wrote it, I did not quite realise that ‘scale’ is close to the dictionary meaning of the word ‘gauge’, even though I vaguely recall having read the use of word gauge by Einstein when he attempted unification of Gravity with electromagnetism. Or may be ‘gauge’’ was first used by Weyl.

Even google does not return much for ‘gauge’ independently, and the word is always associated with transformation, invariance, freedom, field, condition...... Or, when one says, the gauge is Lorenz, or Coulomb, one puts a mathematical definition to this. The best for me is: choosing a gauge is choosing a condition which fixes potential(s).....equivalently, gauge is a ‘scale’. But as mentioned to Adil above, there are problems in this definition. In an attempt to make the students with a given background knowledge understand what is being said, sometimes we make compromises, while widening their horizon.

I spent a little time reading a few paragraphs from this: https://arxiv.org/vc/hep-ph/papers/0012/0012061v4.pdf,
Which also mentions the first use (gauge invariance) by Weyl.

But my original question stays: left to itself, what does the word ‘gauge’ mean in Physics? And I think scale is closest, albeit incomplete. I think ‘gauge’ has a meaning only when associated with one of the other words mentioned above.
N D Hari Dass
N D Hari Dass still misses the most important aspect of gauges i.e redundancies in the descriptions of states
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Ashok Kapoor
Wonderful. It is rare to have a discussion like this on facebook. I will copy and paste all of it in a blog on
http://0space.org
 
 
Jayant Singh
Jayant Singh Image result for what is gauge in physics
Gauge theory. ... In physics, a gauge theory is a type of field theory in which the Lagrangian is invariant under certain Lie groups of local transformations. The term gauge refers to any specific mathematical formalism to regulate redundant degrees of freedom in the Lagrangian.
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Jayant Singh replied · 4 Replies
Jasjeet Singh Bagla
Jasjeet Singh Bagla My understanding is that you have gauge freedom when you have more degrees of freedom in your equations than you actually do in the theory. This can result from presence of symmetries. In such a case, there are multiple valid ways of 'reducing' the degrees of freedom and get on with life.

So you have gauge freedom when you have certain symmetries in the problem. You make a choice of how to exploit the symmetry to remove redundancy in the equations, this is the choice of gauge.
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Sudhir Raniwala
Sudhir Raniwala Thanks, Jasjeet. This is attended to in the discussion above. Please read my response to Gautam Menon, and to Pankaj Sharan.
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N D Hari Dass
N D Hari Dass not satisfactory..lagrangeans are also invariant under rotations but rotations are not gauges..in fact, your answer is even wrong in the sense that gauge invariances are not symmetries..refer to my imsc talk recently on this important, but often misunderstood subject
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Sudhir Raniwala
Sudhir Raniwala N D Hari Dass please share the link / file. Thanks.
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N D Hari Dass
N D Hari Dass Sudhir Raniwala traveling at the moment..will do so at the earliest

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