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The charge of a fundamental particle is a mysterious but obvious and well-known property of every non-neutral particle.

I can understand how, if a particle is an object, or thing, for want of a better word, in its own right, then it can have a property of charge, because it would just be a property that's attached to the object (particle).

However, I think it was Brian Cox or Roger Penrose (not entirely sure which) who said in a book or on television, that a particle is just a point of high intensity in a quantum field.

How can it have charge if it's just an intense point in a quantum field? Surely the high intensity couldn't just result in charge.

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If possible could you find the specific reference for Cox or Penrose? Just want to see what was actually said. – user11547 Feb 25 '13 at 0:28
No, I'm afraid not, but I can guarantee you that the quote was "a particle is a point of high intensity in a quantum field" - I was rather surprised and therefore haven't forgotten. – ODP Feb 25 '13 at 22:59

My preferable answer would have to do with the topological properties of the vector bundle to which this field belongs, but a easier way to think about it might be that charge is a property of the field itself, not of the 'high intensity point'. High intensity would suggest that a higher-intensity concentration would result in a larger charge, which is not true for fundamental particles like electrons or whatever.

So think of the electron field as having a charge of -e. This electron field permeates everything everywhere, and in some places it forms point-like excitations ("high intensity points") where we actually measure the presence of the electron. There, we can tell the field has a charge of -e.

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Not only the electric charge, but also the mass of a particle is a high “concentration” in the quantum field.

If we take an electron for example, we know its electric charge, $e\sim-1.6\times 10^{-19}$C and its mass, $m_e\sim 9.1\times 10^{-31}$ Kg. However, the electron lives in the quantum world and obeys the rules of quantum mechanics. Before the electron is observed at some place in space at some time t, nobody knows where it can be. Nature tells us that the only sensible thing to do is to assign a probability to find it at some point in space. Hence we solve Schrodinger’s equation, and when we do that we know the probability amplitude $\Psi({\bf r},t)$. The wave function then gives the electric charge and mass density for the electron as

For the electronic charge: $\rho_e({\bf{r}},t)=e|\Psi({\bf r},t)|^2$

For the electronic mass: $\rho_m({\bf r},t)=m_e|\Psi({\bf r},t)|^2$.

The point in space where $|\Psi({\bf r},t)|^2$ is the highest, shows where it is more likely to find the particle, and upon a measurement we will find the total charge and the mass of the electron at that point. This is associated with the process called the collapse of the wave function of the particle at the point of observation.

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