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Relationship Between QED/QCD and Field Theories 
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#1
Dec1312, 05:47 AM

P: 149

Are QED/QCD themselves field theories or subfield theories of other more general field theories?
What are the formal theories/theoretical frameworks that completely characterise the Standard Model in our present state of knowledge? IH 


#2
Dec1312, 03:41 PM

P: 883

QED and QCD are specific quantum field theories. You might read:
http://en.wikipedia.org/wiki/Classical_field_theory http://en.wikipedia.org/wiki/Quantum_field_theory "Quantum field theory" is the general mathematical framework that we've found most useful in particle physics. Quantum field theory provides a generic way of discussing particles and their interactions taking into account both quantum mechanics and relativity. The Standard Model is a specific quantum field theory, where we postulate the existence of a certain set of particles and interactions to explain all the observations we've made. QED, which describes the electromagnetic force, and QCD, which describes the strong force, are both "subtheories" of the standard model, which includes both the electromagnetic and strong forces. 


#3
Dec1312, 03:56 PM

Mentor
P: 12,072

Well, QED is the lowenergy theory of the electroweak interaction, which combines electromagnetic and weak force into one. The SM contains the known elementary particles, QCD, the electroweak interaction and its symmetry breaking via the Higgs mechanism. All is expressed as quantum field theory.



#4
Dec1312, 05:12 PM

P: 149

Relationship Between QED/QCD and Field Theories
Many thanx for the kind feedback. Just to round off my comprehension, can you kindly confirm:  Quantum field theory in general as well as its QED/QCD incarnations are all necessarily defined as gauge theories;  There is at present no established (ie, non speculative) quantum gravity field theory and  Conformal field theory does not concern itself with the SM but is purely a beyondtheSM theory. IH 


#5
Dec1312, 05:18 PM

P: 149

IH 


#6
Dec1312, 06:30 PM

P: 883

In the context of quantum field theory, gauge theories are just one way of producing interactions between particles (that is, forces. The electromagnetic, strong, and weak forces are all the results of gauge interactions). But there are other kinds of interactions, like Yukawa interactions (which the Higgs boson experiences): http://en.wikipedia.org/wiki/Yukawa_interaction Of course, whatever the "true theory" is, it is clearly well approximated by a quantum field theory, namely the standard model. 


#7
Dec1312, 06:43 PM

Sci Advisor
P: 2,470

First of all, both GR and standard model make extremely good predictions. It can't be random. However, GR is a nonlinear theory. Pretty much any field theory can be approximated by a linear field theory, in which case you can build a quantum field theory. So given that GR works, and based on general Ocam's razor principle, I would guess that success of SM is due to linear approximation working very well due to relatively low energy scales involved. (Low compared to what? Good question.) In which case, a better field theory would be a nonlinear one, and nonlinear field theory cannot be a quantum field theory. But this is more of what we should be aware of, and perhaps looking for in highenergy experiments, rather than any kind of statement on quality of Standard Model. So far, everything we've done confirms SM. P.S. Oh, and even if we discover that underlying fieldtheory is nonlinear, Quantum Mechanics and Standard Model aren't going anywhere. Linear theories are nice. We can actually compute stuff with them. Compare all the nifty things we've done with QM to stuff we've been able to do with GR. Heck, even in GR, Linearized Gravity is an extremely powerful tool that's used for many predictions. 


#8
Dec1512, 10:17 AM

P: 149

Very interesting your comment "Pretty much everything past Classical Mechanics is a field theory of some sort or another". So field theory really constitutes the bulk of modern elementary/particle physics (SR I take it does not need a field theoretic framework, does it?). How about string and other beyondtheSM theories, are they also mostly field theories or not? Finally, regarding your use of the term "noniinear", is this in the simple intuitive sense that x is a linear coefficient and x^2 is not or it is more complicated than that? IH 


#9
Dec1512, 10:23 AM

Mentor
P: 12,072

GR is a (nonlinear) field theory.



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