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• CommentRowNumber1.
• CommentAuthorUrs
• CommentTimeSep 27th 2012
• (edited Sep 27th 2012)

needed matter to point somewhere

• CommentRowNumber2.
• CommentAuthorzskoda
• CommentTimeSep 27th 2012
• (edited Sep 27th 2012)

Now there is “gauge theory with matter field” and “gauge theory without matter field”. Any comment different from what I can already find in the entry ? (I am asking because a student of mine is prepareing a seminar at the moment and wants to be clear about the meaning in this particular context).

• CommentRowNumber3.
• CommentAuthorUrs
• CommentTimeSep 27th 2012

I am in a haste right now. Will reply later. But could you say in more detail what the question is?

• CommentRowNumber4.
• CommentAuthorzskoda
• CommentTimeSep 27th 2012
• (edited Sep 27th 2012)

Well, connection is at start given on a principal bundle $P$. Now matter field is given by a section of an associated spinor bundle (associated to the same principal bundle). Now when we do elementary “derivation” of gauge interactions there is more than one possibility, and the standard one corresponds to what physicists call “minimal coupling”. It may be imagined that if we have a bundle carrying connection and some other spinor bundle, then the possibility that that other bundle is the associated bundle is not the only possibility which ensure forming a term in Hamiltonian out of a connection and a section of the latter bundle, which is behaving as a scalar. Is there a proof that a reasonable coupling between matter and connection can exist only if the spinor bundle is the associated bundle of the principal bundle with connection ? (this may or may not be related to my remark on minmal coupling)

• CommentRowNumber5.
• CommentAuthorUrs
• CommentTimeSep 27th 2012

I don’t know much about non-minimal coupling, only that it does not seem to appear in nature. Sorry.

But I wrote a brief general-purpose paragraph now at minimal coupling.

• CommentRowNumber6.
• CommentAuthorzskoda
• CommentTimeSep 27th 2012
• (edited Sep 27th 2012)

I do not know for sure, but I think there are many effective field theories with application where there are effective fields with non-minimal couplings. I listened some conversations by experts who could list many examples (some classical and some even coming from brane dynamics). I am not able to exhibit this. I am not sure however, if this is related to taking other bundles or not, and if there is an argument about the latter.

• CommentRowNumber7.
• CommentAuthorTobyBartels
• CommentTimeSep 27th 2012

On related entries: I've long thought that it's wrong to contrast matter with energy. Energy is a measure of stuff (using the word ‘stuff’ quite broadly), like mass, not stuff itself, like matter. Sometimes people say that mass measures the amount of matter, while energy (as a measure) measures the amount of energy (as stuff), but that's not really true, especially since gauge bosons can have mass and matter has energy (even rest energy). If we must contrast matter with something, it would be better to use radiation (a suggestion that I read somewhere else, I forget where).

• CommentRowNumber8.
• CommentAuthorUrs
• CommentTimeSep 28th 2012
• (edited Sep 28th 2012)

Toby, I’d agree with that, I think. But: is this referring to some nLab entry, or just a general statement? If the former, which one?

it would be better to use radiation (a suggestion that I read somewhere else, I forget where).

That’s certainly the use of terminology in FRW model cosmology: here the ratio $w = p/\rho$ of pressure over density characterizes the different source of energy-density, $w = 1/3$ is “radiation” while $w = 0$ is “dust matter”.

I just put in a note on this at FRW model.

• CommentRowNumber9.
• CommentAuthorTobyBartels
• CommentTimeSep 28th 2012
• (edited Sep 28th 2012)

My comment references the Related Concepts section at matter (which you just edited in light of it, so OK).