We have a theory of a Higgs field that describes how a particle gets mass. Since mass and charge both are intrinsic properties of a particle, is there any similar theory for how particles get electric charge?
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6$\begingroup$ Mass and charge are not both intrinsic properties. Charge is an intrinsic property but mass isn't. Above the electroweak transition the mass of all fundamental particles goes to zero but the charge is unchanged. $\endgroup$– John RennieCommented Jul 31, 2013 at 18:17
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2$\begingroup$ In KK theories, quantized momentum in the 5th dimension behaves like electric charge. $\endgroup$– DilatonCommented Jul 31, 2013 at 22:34
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1$\begingroup$ @JohnRennie what do you mean by above the electroweak transition the mass of all fundamental particles go to zero? I do not understand this ... :-/ ? Of course is the mass of a particle an intrinsic property of an elementary particle. $\endgroup$– DilatonCommented Jul 31, 2013 at 22:53
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3$\begingroup$ We need to carefully define "particle," and "intrinsic property" in order to avoid talking past each other (as is already starting to happen). John Rennie is correct if by "particle" he means any discrete excitation of a given field and by "intrinsic" he means "not determined by any interactions with other fields." Dilaton and the OP are correct if by "particle" they mean "low lying discrete excitations on the vacuum which may involve a combination of several fields" and by "intrinsic" they mean "eigenvalues of a quadratic Casimir of the Poincare group acting on a single particle irrep." $\endgroup$– MichaelCommented Aug 1, 2013 at 5:06
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3$\begingroup$ Also I'll add in response to @JohnRennie that it is a common mistake that the "particles" (meaning excitations of individual standard model fields) are massless above the electroweak phase transition. It is true that the Higgs vev goes to zero so there is no longer any tree level mass, but there is a thermal mass of the order $g^2 T$ where $g$ is a gauge coupling constant and $T$ is the temperature. If what you care about are the low lying (quasi)particle excitations over the thermal state then this is the mass that counts. $\endgroup$– MichaelCommented Aug 1, 2013 at 5:12
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2 Answers
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Your question is very good. The answer is very easy, but very deep though.
"Charge $Q$" means that there is a conserved (quantum or classical) number $Q$ respect to some symmetry $G$. i.e. the system is invariant respect to certain symmetry $G$ transformation. (You can derive it from Noether theorem or simply the transformation on the "fields" in general, providing there is no quantum anomaly due to path integral Jacobian varies or the anomalous currents.)
So the origin of the "Charge $Q$" is due to the conservation of some symmetry $G$.
The symmetry can be gauge (local) symmetry or global symmetry. The gauge can be the normal small gauge or the large gauge transformation. The large gauge transformation is very similar to the type of global symmetry transformation.
ex:
1. In E & M, we have U(1) gauge symmetry. We thus have electric charge $e$, $-e$.
2. In QCD, we have SU(3) gauge symmetry. We thus have three color charge $r$, $g$, $b$ and its anti-colors.
3. In quantum gravity, some people had believed there is no global symmetry, everything is local gauge symmetry.
In short,
Q: Is there any theory for origination of charge?
A: Yes. There is, the theory of symmetry.
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1$\begingroup$ (Noether) charge does not arise from a local symmetry, but only from a global symmetry. $\endgroup$ Commented Mar 8, 2014 at 21:29
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$\begingroup$ I edit: the transformation on the "fields" in general. But can Frederic you tell why the Fujikawa method for path integral capturing chiral-anomaly example, is simply the variation on the field with axial transformation, but we call this a Adler-Bell-Jackiw U(1)A "gauge" anomaly? In this sense, what Fujikawa did is simply the Noether theorem on the whole path integral or partition function $Z$, instead of on action $S$. $\endgroup$ Commented Mar 9, 2014 at 2:47
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$\begingroup$ So my point is that gauge anomaly is really very like a the anomaly of weakly-coupling gauge theory, like the anomaly of some global symmetry, like SPT. $\endgroup$ Commented Mar 9, 2014 at 2:49
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$\begingroup$ Because the anomaly is caused by an instanton configuration of the gauge field, which results in a topological index contributing an anomaly coefficient. $\endgroup$ Commented Mar 9, 2014 at 11:15
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$\begingroup$ As i know that symmetry gives the conservation of some defined quantity. How can we describe the origin of that quantity from symmetry. Another point that i want to discuss is that, since mass and energy can be converted in each other (from STR) so, as a symmetry in time give the conservation of energy Is it leads to conservation of mass. $\endgroup$– RahulCommented Mar 12, 2014 at 13:13
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Although theories of electromagnetism (a la Maxwell) and electroweak unification (a la Weinberg, others) work well to explain the behavior of charge / magnetism / electroweak, none of these provide a mechanism for originating electric charge. Similarly, in QCD, which explains the behavior of the strong force between quarks and gluons, no mechanism is described for originating "color charge".
Although the Higgs mechanism certainly gives mass to quarks, electrons, and the W and Z bosons of the electroweak force as the last missing verification of the Standard Model, it does not explain the majority of mass / energy of bulk matter. Most of that derives of virtual particle interactions that occur inside of hadrons and mesons, and for the strong force, something like the Higgs field or mechanism is evidently not required. Neither does the Higgs field or mechanism yet provide us with any deeper insight into the origin of gravitational mass or the riddle of dark matter or dark energy, even though in classical physics, inertial mass and gravitational mass were believed to be intimately related.