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Yes, photons are the quanta of the electromagnetic field. In this picture, two charges create a disturbance in the EM field (which can also be called the photon field). A virtual photon mediates their repulsion. There is more information here.


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The following situation is not uncommon: classically a symmetry may be (spontaneously) broken, but, quantum mechanically, the symmetry is restored. Put differently, quantum fluctuations can, under certain, well understood conditions, destroy the classical asymmetry ("order"). The simplest example is probably the one-dimensional double well potential, ...


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Why not try to draw the Feynman diagrams first and characterize them by different topologies; then count the possible contractions for each cases?


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$\newcommand{\ket}[1]{\lvert #1 \rangle} \newcommand{\bra}[1]{\langle #1 \rvert}$The states of a quantum system are nothing else than the abstract vectors in the Hilbert space of states $\mathcal{H}$. For one particle, given a basis of position eigenkets $\ket{x}$ with $\hat{x}\ket{x_0} = x_0\ket{x_0}$ and a state $\ket{i}\in\mathcal{H}$, the wavefunction is ...


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If we know there is a particle(s) in state $i_1$ why do we need $r_1$? Does the state $i_1$ not specify position? The fact that the particle is in a state $|\psi\rangle$ does not specify the particle's position - it specifies the wave-function $$ \langle x | \psi \rangle = \psi(x) $$ from which one can find $$|\psi(x)|^2$$ This is the probability ...



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