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QFT vs QM 101by waterfall
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#55
Feb512, 08:54 PM

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Oh yes, there's another interesting point. Actually there is more than one way to make the Dirac and EM fields interact while having EM gauge invariance. The usual "gauge principle" is maybe more informatively called "minimal coupling"  just as the "equivalence principle" of GR is really a "minimal coupling" of matter and metric.



#56
Feb512, 11:33 PM

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#57
Feb612, 01:59 AM

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#58
Feb612, 04:13 AM

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#59
Feb612, 05:23 AM

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PF Gold
P: 9,274

Maybe you could also add additional gauge fields. I'm not sure. I think in that case, it wouldn't be a U(1) gauge theory anymore. 


#60
Feb612, 06:35 AM

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#61
Feb612, 04:44 PM

P: 381

In the context mentioned in this thread. How does QFT analysis differs to condensed matter physics where according to wiki: "These properties appear when a number of atoms at the supramolecular and macromolecular scale interact strongly and adhere to each other or are otherwise highly concentrated in a system.". In normal QFT like QED, we just deal with some photons interacting with electron and you only have a few interactions in the Feynman diagrams (plus those first order perturbations or virtual particles). How about in condensed matter when there are lots of atoms. Any bird's eye view of how the analysis is done?



#62
Feb612, 08:20 PM

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#63
Feb612, 09:53 PM

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#64
Feb712, 07:11 AM

P: 381

Is anyone familiar with this or heard of this concept before? It started in 1953 by a paper by Dicke published in peer reviewed Physical Review Journal called "Coherence in Spontaneous Radiation Processes" http://prola.aps.org/abstract/PR/v93/i1/p99_1 Then in 1973 Hepp and Lieb published in peer reviewed papers "K. Hepp, E.H. Lieb, Phys. Rev. A 8 (1973) 2517. and K. Hepp, E.H. Lieb, Ann. Phys. 76 (1973)" concerning these SuperRadiant Phase Transition in condensed matter. Or by way of summary: "Dicke formulated a model which was later shown to exhibit a superradiant phase transition (by Hepp and Lieb). The notion that such phase transitions should exist in condensed matter systems has been investigated in a series of papers by Preparata and coworkers [4–6] and others [7–9]. Different workers have come to somewhat different conclusions concerning superradiant phase transitions [10–19]. Some doubt has been expressed [20–24] concerning the physical laboratory reality of superradiant phase transition. The mathematical issues are as follows: (i) It appears, at first glance, that quadratic terms (in photon creation and annihilation operators) enter into the model via quadratic terms inthe vector potential A. (ii) The quadratic terms in the “corrected Dicke model” appear to destroy the superradiant phase transition. Then many works show that if the dipole–field interactionis treated in a gauge invariant manner [25–27] then the interaction is strictly linear in the electric field E. Thus, quadratic terms are absent for purely electric dipole–photon interactions [28]. These considerations render likely the physical reality of condensed matter superradiant phase transitions." (from http://arxiv.org/abs/condmat/0007374) What do you make of this? Preparata and others have shown many experimental results. http://arxiv.org/abs/condmat/9801248 http://arxiv.org/abs/quantph/9804006 Has anyone encountered the concepts mentioned in this message before? Can you please comment especially experts in Condensed Matter (and even the not so experts). If confirmed. The implications would be significant. Latest paper concerning the original peer reviewed concept or ideas was just last January 31, 2012 for example in http://arxiv.org/pdf/1108.2987.pdf 


#65
Feb712, 08:03 AM

P: 597

What I'm about to say is a lot more American than my taste in vernacular usually permits, but I'll say it anyway:
Dude, seriously. You can't jump from reading popsci books to speculating on the implications of the latest research published in journals (based purely on abstracts that you, like other people who aren't specialists in the topic of the paper, don't understand), just after 64 posts of discussion on an internet forum. If you want to understand this stuff properly, then perhaps start here. You'll need a pen, paper, coffee, and probably at least 5 years, more if you're only studying in your free time. Get back to us when you get stuck. On the other hand, if you want to get a decent layman's understanding of what QFT is, and how it relates to the ordinary world, great. Here's a good place for that too. But keep it simple, and don't worry about what are essentially technical concepts like Fock space. It's an infinite dimensional vector space expressed as a direct sum of other infinite dimensional vector spaces. That's what it is, and if that doesn't add much to your understanding, then you're asking the wrong question for now. Far better instead to work out why you can pick up the electromagnetic field with your radio antenna, but you can't do the same for the "electron field". 


#66
Feb712, 08:29 AM

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#67
Feb712, 08:42 AM

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#68
Feb1412, 04:45 AM

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P: 303

Also, for example in [tex]\phi^{4}_{2}[/tex], the theory requires a different Hilbert space for each value of the coupling [tex]\lambda[/tex] as proven by Nelson. 


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