
#1
Nov613, 03:17 PM

P: 2,900

I was reading this recent Scientific american article wich I found interesting, and was spurred on by it to ask a couple of questions.
Is the mathematical concept of fundamental point particle currently a basic postulate in physics(let's take as current physics the QM basedQFT modern models)? I'm thinking about mathematical concepts like the Dirac delta and modeling point sources with Green's functions as something necessary to keep linear superposition and QM as a linear theory, (not sure we can talk about the different QFT's being linear or not). Is the field concept in QFT really more fundamental or not? Is the term "particle physics" really a misnomer? How should one picture the high number and diversity of quantum fields,(one for every possible fundamental particle... scalar, vectorial and tensorial... interacting and ad free...)? 



#2
Nov613, 05:11 PM

P: 313

As for whether the name "particle physics" is a misnomer, well, I don't really think so, since one only ever deals with the particles. The existence of the underlying fields is only indirectly inferred. "How should one picture the high number and diversity of quantum fields"  I don't exactly know what you are looking for. They are just there, all "sitting on top of each other" at every point of spacetime. They might all be different degrees of freedom of some more fundamental underlying field though, or of some compactified dimensions of spacetime etc, string theory style. So back to the first question: the quantum fields are pretty much a postulate of quantum field theory, yes. It isn't exactly formalised that way, there are games one plays reconciling standard quantum mechanics with special relativity and it works out that these quantum fields emerge as the solution for doing that, but you can more or less take them as a postulate I think. 



#3
Nov713, 08:49 AM

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#4
Nov713, 09:10 AM

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Fundamental particles in physics 



#5
Nov813, 04:57 AM

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#6
Nov813, 10:04 AM

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Conversely, one could say the single Dirac field leads to two related particles  electron and positron. Just depends on how you count things. 



#7
Nov813, 11:23 AM

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#8
Nov813, 11:32 AM

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#9
Nov813, 04:03 PM

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#10
Nov813, 04:56 PM

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E_R (1,1) for a total of 1 field L_L (2,1) for a total of 2 fields U_R (1,3) for a total of 3 fields D_R (1,3) for a total of 3 fields Q_L (2,3) for a total of 6 fields, So if you count a multiplet as a single field, you have 5 different fields and if you count each individual member of a multiplet as a separate field, you have 15 fields. There is no way to get only four fields. Those fields lead to only four standard model particles as I mentioned earlier. All these fields are chiral fields and are accordingly labeled either with a "_L" or with a "_R". The first two fields are lepton fields while the last 3 are quark fields. The electron mass is generated by the interaction E_RL_LHiggs, the up quark mass is generated by the interaction U_RQ_LHiggs, and the down quark mass is generated by the interaction D_RQ_LHiggs. One of the components of L_L is left unpaired leading to a massless neutral particle  the neutrino (which is not a Dirac spinor in the Standard Model). 



#11
Nov813, 08:21 PM

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That's supersymmetry, which is beyond SM. None of this is true in SM.
Also, electron current mass is generated via interaction with Higgs. Same for the quarks. Most of the mass is actually dynamically generated. But that's aside from the discussion. 



#12
Nov813, 08:48 PM

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#13
Nov813, 11:51 PM

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dauto is correct. Furthermore, if you take the hermitian conjugate of a L field, you get a R field (in the complexconjugate rep of the gauge group), and viceversa. So it's just a matter of convention that some fields are listed as L and some as R; we could list them all as L. This is all explained in great detail in Srednicki's QFT text.




#14
Nov913, 07:04 AM

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