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Leaving out numerical factors, we have that $$ \mathrm{d}j_A = \mathrm{Tr}(F \wedge F)$$ This already shows that we are dealing with a topological quantity, since the RHS is the second Chern character of the gauge field (or rather, the principal bundle associated to it). Now, there is also the (3D) Chern-Simons form $$ \omega = \mathrm{Tr}(F \wedge A - ...


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If you assume separability of the wave function, i.e., $\psi(\mathbf x)=u(x)v(y)w(z)$, you can solve the individual components separately: \begin{align} -\frac{\hbar^2}{2\mu}\frac{d^2u(x)}{dx^2}+V_1(x)u(x)&=E_1u(x)\\ -\frac{\hbar^2}{2\mu}\frac{d^2v(y)}{dy^2}+V_2(y)v(y)&=E_2v(y)\tag{1}\\ ...


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In the case of QCD there is asymptotic freedom, meaning that though the theory is strongly coupled at low energies (such that we still cannot analytically calculate how the atomic nucleus stays together) the coupling becomes less and less as we go to higher and higher energies. This means that the ultimate picture of the behavior of quarks is a weakly ...


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Instantons are characterized by the winding number and a set of collective parameters (e.g. location of the centers of the instantons, their sizes and the inequivalent orientations in the global group space / space-time). Quantum fluctuations of a unit winding number instanton can either leave the collective parameters unchanged (non-zero modes), or change ...


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No. Feynman diagrams are made by summing over the perturbative contributions of quantum amplitudes. They cannot hold non-perturbative information.


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A vacuum is a field configuration that is pure gauge, i.e. $A = g^{-1}\mathrm{d}g$ for a gauge transformation $g$, and hence $F = \mathrm{d}_A A = 0$ (for $\mathrm{d}_A$ the gauge covariant derivative). An instanton is a local minimum of the action, which is given by an (anti-)self-dual configuration $F = \pm \star F$. It is not a vacuum for non-zero ...



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