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Does the field of a set of photons behave differently from a single photon.

e.g. Suppose I have a group of photons with their Electric fields $\mathbb{E}_n$ all aligned. So $$\mathbb{E}_{\text{tot}} = \mathbb{E}_1 + \mathbb{E}_2+ \text{...} + \mathbb{E}_n$$

and upon this field a single photon with parallel $\mathbb{E}_i$ field is incident. Does $\mathbb{E}_i$ scatter?

Or do I require such a large number of photons in $\mathbb{E}_{\text{tot}}$ that the field polarizes the underlying quantum vacuum to produce particle pair that scatter the $\mathbb{E}_i$ particle.

More simply put, can an electric field by itself scatter a photon?

Urb
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metzgeer
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2 Answers2

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To be slightly pedantic, there isn't really such a thing as the field of a photon, if you think of photons as being things we can count.

The state $|p\rangle$ in the Hilbert space of the quantum Maxwell theory is a superposition of all possible states where the EM field has a definite value. This is because the field operator is a superposition of photon creation and annihilation operators. So if the EM field has a definite value, we aren't in an eigenstate of the photon number operator.

That said, there is such a thing as photon-photon scattering in particle physics. Two photons can scatter via intermediate virtual processes in the Standard Model. The effect isn't very strong though, so we don't see it at ordinary distance scales.

user1504
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''More simply put, can an electric field by itself scatter a photon?''

Yes, though the dominant processes are higher order nonlinear effects and hence quite weak; still too weak to be detected experimentally. But this may change soon. Some representative papers:

However, there are experimental observations of virtual photon-photon interactions from electron-positron collisions producing hadrons; see, e.g., https://arxiv.org/abs/hep-ex/9906039.

Urb
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Arnold Neumaier
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