# Gauge Boson for Magnetism

#### jaydnul

I always thought that magnetism was the exact same thing as electricity because of SR. That's probably why I am confused about the search for a magnetic monopole, as well as the classical view of light being perpendicular magnetic and electric fields. So I have a few questions.

1. What is the gauge boson for magnetism? What particle is being exchanged when there is a magnetic force? Because in an electric force, the photon is being exchanged, correct?

2. If the photon is also the gauge boson for magnetism, then wouldn't that just make it electricity and we can just discard the term magnetism all together?

3. By that reasoning (which is probably wrong), why don't we say that the weak force is also mediated by photons due to the recent unification with electromagentism?

Thanks

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#### jtbell

Mentor
At the quantum level, electromagnetism is a single interaction whose gauge boson is the photon. Both electric and magnetic interactions can be thought of as mediated by virtual photons. Whether a particular interaction is electric or magnetic or both depends on your reference frame according to the Lorentz transformation.

In the limit of classical electromagnetism, we call the part of the electromagnetic force that depends on the particle's velocity, "magnetic", and the part that doesn't depend on the particle's velocity, "electric".

#### PeterDonis

Mentor
I always thought that magnetism was the exact same thing as electricity because of SR.
A better way to say it would be that electricity and magnetism are aspects of the same thing, electromagnetism. In the general case, both will be present. (In cases where it seems like there's only magnetism present, there actually is electricity present, it's just not directly observed.)

1. What is the gauge boson for magnetism? What particle is being exchanged when there is a magnetic force? Because in an electric force, the photon is being exchanged, correct?
The photon is the gauge boson for electromagnetism, so both electricity and magnetism involve the exchange of photons.

2. If the photon is also the gauge boson for magnetism, then wouldn't that just make it electricity and we can just discard the term magnetism all together?
This is really a matter of terminology, not physics. The usual terminology is what I used above: "electromagnetism" is the general term that covers all types of photon exchanges, and "electricity" and "magnetism" are more specific terms that only apply to certain kinds of photon exchanges.

3. By that reasoning (which is probably wrong), why don't we say that the weak force is also mediated by photons due to the recent unification with electromagentism?
Because it isn't. The weak force and electromagnetism are both aspects of a more general force, the electroweak force. At high energies (such as in the early universe), this unification is manifest and there are four massless gauge bosons that mediate the electroweak force. But at low energies, such as in our universe at present (unless we create special conditions, such as inside particle physics experiments), the symmetry of the electroweak force is broken and it appears as two separate forces, electromagnetism (mediated by the massless photon) and the weak force, mediated by three massive gauge bosons, usually referred to as $W^{+}$, $W^{-}$, and $Z$.

#### WannabeNewton

I always thought that magnetism was the exact same thing as electricity because of SR.
This is actually very incorrect conceptually. SR says no such thing. What it really implies is the decomposition of the electromagnetic field into electric and magnetic parts depends on the choice of reference frame so that e.g. if the field configuration lends to a purely Coulombic part in one frame it can have both electric and magnetic parts in another under a Lorentz boost.

Because in an electric force, the photon is being exchanged, correct?
This is actually a more subtle question than it seems at face value. Let me start by saying, no in the case of an electrostatic force it is not a photon, in the usual sense of the term, that is being exchanged. When people normally say photon what they really mean is transverse photon. In a Lorentz covariant description of the Feynman propagator in QED, which fully describes scattering processes between charged particles interacting through an electromagnetic field, there are in fact three different kinds of photons.

There are the two transverse photons (one for each polarization mode), one scalar photon, and one longitudinal photon. The transverse photons correspond to radiative modes and are what you typically imagine when drawing external photon lines in a Feynman diagram but real photons (external lines) are different from virtual photons (internal lines) in that they only have transverse modes; when drawing internal lines for virtual photons (Feynman propagator) you must take into account the longitudinal and scalar modes as well (see below). Thus, as you can probably imagine, it is not only the transverse photons that are conceptually important in QED. Indeed, the longitudinal and scalar photons are what together describe the electrostatic force, which is an instantaneous force.

For a real photon, the longitudinal and scalar modes can be entirely gauged out by an appropriate choice of gauge (Coulomb gauge + an additional constraint). This essentially comes from the fact that real photons are massless. But for virtual photons we have more leeway since they are off-shell (they do not satisfy $p_{\mu}p^{\mu} = 0$) and do allow for longitudinal and scalar modes thus giving rise to the electrostatic interaction. The retardations in electromagnetic interactions, that is, the dynamical degrees of freedom, are then described by the two transverse modes which are, as stated above, radiative.

#### MrRobotoToo

A gauge boson is present only when there is a locally gauge invariant interaction. Magnetism by itself is not locally gauge invariant.

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