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Just to complement Ali Moh's answer: We can define a topological current in the same way we do for the $\phi^4$ kink, $$J_\mu=C\epsilon_{\mu\nu}\partial^\nu\phi(t,x),$$ where $C$ is a normalization constant and $\epsilon_{01}= -1$. The topological charge then is $$Q=\int_{-\infty}^\infty J_t dx=C\int_{-\infty}^\infty\partial_x\phi ...


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You have to define what a soliton is. The most accepted definition in field theory is that a soliton is a stable, localized and finite energy/energy density solution of the equations of motions of the theory. A vortex ring is localized in space, it has finite energy and definitely is the solution of some equation of motion. Then if it is stable, it can ...


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My 2 cents on it is that in QM (be it "standard" QM or QFT) one describes only the state of a particle. Having said that, the most general state for a single particle is indeed a wave packet. Now, if you localise certainly a particle at some point in time, then later on it will be associated with a spreading wave packet because of Heisenberg indeterminacy ...


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A particle is not a wavepacket. And there are no particle states for interacting theories. We define particle states in QFT by expanding the free field into its Fourier modes and using these modes as creation/annihilation operators for particle states - the mode of momentum $p$ creates the particle state $\lvert p\rangle$ with momentum $p$. The Hilbert ...



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