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Beautiful (in my opinion) source in which higgs mechanism nature of superconducting phenomena is discussed, is Steven Weinberg's QFT Vol. 2, sec. 21.6. Topological nature of superconucting vortices is discussed in this section. Also, there is general discussion on topological configurations in QFT, with theoretical minimum, in Chapter 23.


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Let us consider scalar electrodynamics (Klein-Gordon-Maxwell electrodynamics) with the Lagrangian: \begin{eqnarray}\label{eq:pr6} \nonumber -\frac{1}{4}F^{\mu\nu}F_{\mu\nu}+\frac{1}{2}(\psi^*_{,\mu}-ieA_\mu\psi^*)(\psi^{,\mu}+ieA^\mu\psi)-\\ -\frac{1}{2}m^2\psi^*\psi \end{eqnarray} and the equations of motion \begin{equation}\label{eq:pr7} (\partial^\mu+...


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Let me explain @ACuriousMind 's answer with some verbiage. The short, regrettably oracular, answer is that the Fabri-Picasso theorem does not hold in a finite superconductor, since translational invariance fails at its boundaries. Really, I do appreciate this is aggressively obscure: will strive to explain. First of all, if you have a chunk of warm ...


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(In my experience this tends to be a rather controversial subject, so I think this answer might start some arguments!) First of all, given a specific action, it is a purely mathematical result whether or not there exists a local transformation that depends on an arbitrary smooth function $\lambda(x)$ on spacetime and leaves the action invariant. The ...


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Gauge theories describe the connectivity of a space with small, symmetric extra dimensions Start with an infinite cylinder (the direct product of a line and a small circle). The cylinder can be twisted. To avoid appealing to concepts that I'm trying to explain, I'll just say that the cylinder is made of wire mesh: evenly spaced circles soldered to wires ...


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Here's the most elementary example of a gauge symmetry I can think of. Suppose you want to discuss some ants walking around on a Möbius band. To describe the positions of the ants, it's convenient to imagine cutting the band along its width, so it becomes a rectangle. Then you can tell me where an ant is by telling me three things: Her latitude—her ...


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There is very interesting physical interpretation of the gauge invariance in the case of $U(1)$ symmetry. Gauge symmetry is the only way to obtain Lorentz invariant interaction of the matter (in the wide sense - the field of arbitrary spin) and photons (being massless particles with helicity 1), which decreases as $\frac{1}{r^{2}}$ at large distances (this ...


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These calculations very often depend only on the difference between two values, not the concrete values themselves. You are therefore free to choose a zero to your liking. Is this an example of gauge invariance in the same sense as the graduate examples above? Yes indeed it is, in the most general definition of gauge invariance, it's what physicists call a ...


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The reason that it's so hard to understand what physicists mean when they talk about "gauge freedom" is that there are at least four inequivalent definitions that I've seen used: Definition 1: A mathematical theory has a gauge freedom if some of the mathematical degrees of freedom are "redundant" in the sense that two different mathematical expressions ...


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Since you mentioned coming from a mathematics background, you might find it nice to take an answer in terms of equivalence classes. A gauge theory is physical theory where the observable quantities, as in, things you could measure with an experiment given perfect measuring equipment, are equivalence classes in a vector space. Electromagnitism is the most ...


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I only understood this after taking a class in general relativity (GR), differential geometry and quantum field theory (QFT). The essence is quite trivial, actually: You have a theory that is invariant under some symmetry group. So in quantum electrodynamics you have a Lagrangian density for the fermions (no photons yet) $$ \mathcal L = \bar\psi(x) [\mathrm ...


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In Classical Electrodynamics (CED) the gauge invariance means independence of the electric and magnetic fields from a particular "choice" of the potentials $\varphi$ and $\bf{A}$. The equation for potentials depend, of course, on the particular choice of the "gauge", and they give different solutions for different gauges. In QM and QED the gauge invariance ...


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Gauge invariance is simply a redundancy in the description of a physical system. I.e. we can choose from an infinite number of vector potentials in E&M. For example, an infinite number of vector potentials can describe electromagnetism by the transformation below $$A(x) \to A_\mu(x) + \partial_\mu \alpha(x)$$ Choosing a specific gauge (gauge fixing) ...


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Expanding on my comment, I think the Rarita Schwinger field (spin 3/2) has exactly the gauge symmetry you want: https://books.google.be/books?id=KFUhAwAAQBAJ&lpg=PA96&ots=vh0WtWM5rg&dq=rarita%20schwinger%20fermionic%20gauge%20symmetry&pg=PA95#v=onepage&q&f=false This gauge symmetry removes the spin 1/2 component of the field so only ...


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Imposing local gauge symmetry on the Dirac equation produces the electromagnetic field interacting with it. See http://www.physics.rutgers.edu/~steves/613/lectures/Lec06.pdf Before any down voting please see my comments below. The question was not about we whether Dirac's equation can be used to represent a spin 3/2 or higher fermion, though you could ...



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