Question: I recently read an article, I think in Scientific American, on the role of gauge fields in solar flares. How would gauge fields relate to powerful
solar flares?
Answer: Lacking a specific citation (issue, date, title etc.) with the necessary elaboration, the question is not really answerable in a solar physics or astrophysics context. Basically, what you would need to do is present far more details from the piece you read and elaborate the case made. But it appears you are unsure of the source you actually saw it.
While it is true there is a fundamental relation between gauge fields and plasma physics, and plasma physics underlies solar flares, the objects of inquiry are vastly different. So while the electric and magnetic fields peculiar to plasma physics are themselves classical gauge fields, no solar physicist uses gauge fields to describe solar flare dynamics, nor will you see him using the term 'plasmons' (for the quanta of longitudinal plasma oscillations.)
In standard plasma physics, the dynamics are driven by
Maxwell's equations which can easily be integrated into plasma dynamics of flares. However, specific gauge fields are far less amenable and out of place in flare theories. One could say the language is incompatible as well as the objects of inquiry.
One is more likely to
find them in formulations like Quantum Electrodynamics (QED), and also references
to electromagnetism as the simplest Abelian gauge theory (specifically, with a U(1)
symmetry). The photons that mediate these interactions are the gauge bosons.
But no one doing flare physics uses the term gauge bosons.
The
problem in addressing it arises because the Wikipedia link you gave shows absolutely no
citation reference for the term - so it is possible the author coined it himself- or interpreted it in a different context. Does it have special meaning? We may never know unless he
himself explains it. I am in no position to since I have no idea what he means by "using gauge fields in flare physics"-
anymore than if he used the term: "superflare plasma
instability vortex".
However, if you are interested in pursuing the gauge field aspect, on consulting a book I have entitled 'Gauge Fields' there is a chapter on 'Asymptotic Freedom' in connection with
energies associated with gauge fields.
It is noted that "grand unification" can be constructed on the basis
of the SU(5) group. At this level of energy - "all interactions are
combined". Meaning that we are probably looking at the very hottest
temperature in the Big Bang itself where all the forces were still unified. (Again, this is all much more fundamental physics than solar flare plasma theory!)
How much more fundamental? In advanced group theory, objects such as spheres are identified with one or
more planes of symmetry. The effect of this is to identify different symmetric
groups through transformations. Among the most common such groups in physics are:
U(1) - > electromagnetic force
SU(2) -> weak nuclear force
SU(3) -> strong nuclear force
All of which have very significant importance in high energy and particle
physics. For example, one might be looking at the transformation of a quantum
wave function (U) such that:
U(t) = exp [-iHt/ħ]
Where U(t) is the unitary time-evolution operator, where i is the usual imaginary number, H is the Hamiltonian, ħ is the modified Planck constant (i.e. h/ 2p. ) Unitarity ensures that the total probability of finding a particle remains exactly 1.
The (1) identifies one particle (boson) which mediates the associated field for
this group. For U(1) that is the electromagnetic field, and the boson is simply
the photon. For SU(2) and any SU(n) where n is a whole number , we can
associate a unitary matrix of size (n x n) with determinant 1. Thus, SU(2),
associated with the weak nuclear force (responsible for radioactive decay)
requires a format such that a typical group member is:U = exp(-i M)
where M is now a 2 x 2 matrix of zero trace. Remember the trace of a matrix M
is the sum of the diagonal entries, viz. Tr(M) = a11 + a22 + a33. The applicable matrix would look like this:
Following the same rubric as above, SU(3)- associated with the strong nuclear
force, means that the matrix M (as defined in the earlier example for SU(2))
now has a 3 x 3 element size. This 3 x 3 matrix can now be resolved into eight
(8) independent component matrices (instead of only three), each of which
corresponds to a charge, so there are now eight charges in all: G1 .......G8,
called 'gluons'. Putting all together:
SU(3) x SU(2) X U(1)
Note this represents lower energy than achieved at SU(5)!
One has a symmetry system which embodies all the gluons (for the strong nuclear
force) as well as the vector bosons for the unified electro-weak force (SU(2) x
U(1)) which subsumes the weak nuclear force as well as the electromagnetic
force. This in turn can be subsumed under a 'grand unified' symmetry, ie.
SU(5).
From the rubric we are using, SU(5) must have a defining matrix M of 5 x 5,
that is 5 elements by 5 elements. Its resolution yields a total of 24 separate
matrices which are associated now with 24 different bosons. This is but one
example that would pertain to a GUT or grand unified theory.
Thus, the temperature referred to this (highest) energy embodied in SU(5) would
be that associated with "extra-dimensional gauge freedom" - possibly
because of all the extra dimensions needed to craft the SU(5) matrix.
Again, all of this is to show there is a vast and fundamental difference in the physics usually applied to gauge fields, compared say with the dispersion relation associated with plasma waves. Such a relation implies that a relationship exists between the
plasma frequency w and the wave
number k. If, on the other hand the group velocity the group velocity , V g does not depend on wave number i.e.
V g = ¶ w /¶k = 0
All of this is at a macroscopic level compared say to the behavior of gluons or bosons in a gauge field.
Hopefully, this makes sense!
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