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Does QFT (Quantum Field Theory) apply to magnetic fields?


Peron
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Does the same explanation for the interaction between charged particles, that QED offers, apply to the magnetic field? Is the magnetic field explained as the overlapping of virtual particles.

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Quantum electrodynamics is the quantum field theory that describes all interactions between charged particles and electromagnetic fields. Via perturbation theory one can indeed interpret these interactions via virtual photons.

 

Now, as you probably know the separation of an electromagnetic field into an electric and magnetic fields is not Lorentz invariant as where QED is. You don't need to worry too much about electric and magnetic fields as separate things. The formalism works for both together.

 

In short, the answer to your question is yes. Electromagnetic phenomena can be understood in terms of virtual photons.

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Does the same explanation for the interaction between charged particles, that QED offers, apply to the magnetic field? Is the magnetic field explained as the overlapping of virtual particles.

 

Your question is not clear. If you mean static magnetic fields, they are classical and do not need any particles to be explained. A classical static magnetic field B is a solution of a static equation with a known current j: B = B(j). It determines the field distribution in space.

 

If you speak of variable magnetic fields that is calculated from QED equations, they are automatically taken into account when one considers charge interaction. It may be "explained" as due to virtual particle exchange. This "explanation" is similar to the Coulomb time-dependent interaction "interpretation" in terms of virtual photons.

 

Factually, however, the magnetic and Coulomb time-dependent interaction terms can be separated from radiation and be still considered as properties of charges rather than virtual photons. This is achieved in the so called Coulomb gauge. It is the charge wave-functions that overlap, not virtual particles.

Edited by Bob_for_short
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Quantum electrodynamics is the quantum field theory that describes all interactions between charged particles and electromagnetic fields. Via perturbation theory one can indeed interpret these interactions via virtual photons.

 

Now, as you probably know the separation of an electromagnetic field into an electric and magnetic fields is not Lorentz invariant as where QED is. You don't need to worry too much about electric and magnetic fields as separate things. The formalism works for both together.

 

In short, the answer to your question is yes. Electromagnetic phenomena can be understood in terms of virtual photons.

 

So, we explain magnets with photons, which are themselves electromagnetic wave packets, isn't that kinda of navigating around the problem?

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So, we explain magnets with photons, which are themselves electromagnetic wave packets, isn't that kinda of navigating around the problem?

 

No. Virtual photons are "attached" to charges. They are not propagating to infinity unlike real photons (wave packets). They are rather different because they are electric and magnetic quasi-static charge interaction terms in the Hamiltonian. They are known also as a "near" field.

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No. Virtual photons are "attached" to charges. They are not propagating to infinity unlike real photons (wave packets). They are rather different because they are electric and magnetic quasi-static charge interaction terms in the Hamiltonian. They are known also as a "near" field.

 

But aren't the force carriers around the electron photons? Photons are bosons right?

 

My question was, if we are trying to explain electromagnetism, why do we say it's made of photons, when photons themselves are electromagnetic? I'm having a hard time understanding.:-(

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Would you see a problem with describing electromagnetism via the electromagnetic field if the electromagnetic field was the description for electromagnetism? Think of the photons being a description for the electromagnetic field.

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Would you see a problem with describing electromagnetism via the electromagnetic field if the electromagnetic field was the description for electromagnetism? Think of the photons being a description for the electromagnetic field.

 

But isn't the photons used to describe what the magnetic field is as well as describe how it attracts? If we call the magnetic field a photon cloud, then we say that Photons are EM wavepackets, then what si the magnetic field that makes the magnetic wave in the Photon?

 

Do you see my confusion here??

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But isn't the photons used to describe what the magnetic field is as well as describe how it attracts?

 

No. It is virtual photons, not real. Real propagate, virtual do not. That is why many avoid employing the term "virtual photons". The good and unambiguous term is a "variable magnetic near-field", not a "virtual photon".

Edited by Bob_for_short
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No. It is virtual photons, not real. Real propagate, virtual do not. That is why many avoid employing the term "virtual photons". The good and unambiguous term is a "variable magnetic near-field", not a "virtual photon".

 

So, what is a magnetic field then?

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So, what is a magnetic field then?

 

Magnetic field is a field determining the magnetic force in the equation of motion of a charge ((q/c)[vxB]) or in equation of motion of a neutral magnet (dipole interaction force).

 

It can be measured and given experimentally or calculated from a given current/magnet data.

 

It is an inter-charge interaction force, if you like. No propagating photons are necessary to explain it.

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So, what is a magnetic field then?
It's just how you "feel" an electromagnetic field when there's relative motion involved. Re the above reference to the near field, the reality underlying the virtual photons of QED is thought to be the evanescent wave. See http://en.wikipedia.org/wiki/Evanescent_wave. Think in terms of a pressure-gradient or "standing wave" for this, as opposed to "propagating waves" for real photons.
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