Is there a quantum theory of magnetism?

henpen

After asking my teachers the same question, I came away with the impression that the classical field model was as far as magnetism went, as if after Maxwell's macroscopic laws there had been no development into a quantum theory of magnetism. Were they wrong? Additionally, if they were to some extent, is there a mediating particle governing magnetism? And how would QED explain the phenomenon?

jambaugh

QED is the quantum theory of the electromagnetic field. Electric and magnet theories are unified. (It just is too much of a mouthful to say "Quantum Electromagnetic Dynamics".) The photon has both magnetic and electric effects and mediates both components of the unified field.

marcusl

Ferromagnetism eluded microscopic derivation from classical principles and was only understood after QM was developed and applied to the problem. Ferromagnetism arises ultimately from long-range couplings between electron spins (themselves a QM concept). Numerous other QM principles play important roles: atomic shell theory and the Pauli exclusion principle, exchange interactions, and Bloch walls, to name a few.

lugita15

It should be noted that before the advent of QM there was an abundance of classical "derivations" of ferromagnetism, paramagnetism, and ferromagnetism. But it was only after the Bohr–van Leeuwen theorem that people came to the conclusion that those derivations were fallacious and that classical explanations don't suffice.

Demon117

Quantum field theory, or Quantum electrodynamics. It is often referred to as the "2nd quantization" or the quantization of the electromagnetic field. It is a beautiful and powerful theory.

sergiokapone

As R. Faynamn was mentioned in his famous lectures (Vol 2, 34):
Thus, for understanding of nature of magnetism it is necessary to include a quantum mechanics. In a frame of classical Maxwell's electrodynamics, it is also considered a magnetic properties of materials, but it is only phenomenologically. The quamtum theory of magnetic properties was developed in Solid State Physics. Fair to say, classical Solid State physics does not exist.

Steger

Yes, the fundamental interactions that drive magnetism are completely and totally quantum mechanical and have absolutely no analogy in classical physics. They derive from some subtle interplay of Fermion statistics, Pauli exclusion principle, quantum tunneling and Coulomb repulsion.

Unfortunately this makes it extremely difficult to make any explanation of magnetism from a classical perspective. Actually there's some interview Feynman did where he basically goes on a bit of a tirade over this exact question because the interviewer wants a simple answer and Feynman basically says he can't give it to him. I'm sure it's on youtube somewhere.

jambaugh

This is absolutely,without qualifications, not true!!! Firstly there is a perfectly good classical theory of electromagnetism with a perfectly good classical mechanical model. See e.g. Maxwell's Mechanical model. Prior to SR one can "explain" magnetism as "vorticity" in the "aether".

The business about the Fermion statistics, PEP, and tunneling is utter nonsense! Magnetism is part of electromagnetism and is explained wholly within the gauge theory of their bosonic mediator the photon. Its effects on other systems may involve e.g. charges, and their statistics, et al but that is secondary. That's the quantum mechanical part.
The photon field has a perfectly well behaved classical limit in the electromagnetic field described by a classical gauge theory. But the gauge business is not necessary to understand and apply the physical theory.

Steger

I'm afraid you're quite mistaken, you are confusing a quantum theory of MAGNETISM with a quantum theory of the MAGNETIC FIELD. These are quite different. The magnetic field can be understood at a classical or quantum level through classical field theory (i.e. maxwell's equations) or QED respectively. MAGNETISM cannot. What is meant by the study of magnetism is the origin of: Antiferromagnetism, Diamagnetism, Paramagnetism, Ferrimagnetism, and, of course, FERROMAGNETISM. These MAGNETIC properties are emergent phenomena of the quantum mechanics of many-body, strongly-correlated, electron systems and can only be derived within this framework. There is NO theory of classical magnetism (they used to think magnetism was due to dipole-dipole interactions but the energy scale for these effects is orders of magnitude too small, ferromagnetism is due to exchange interactions, a quantum effect).

Steger

Perhaps, to clarify a bit more, the words "Quantum Magnetism" do not refer to the quantum field theory of the electromagnetic field but to: Condensed matter field theory, quantum many-body theory, exchange interactions, domain formation, spintronics, superconductivity, quantum phase transitions, etc.

EDIT: In fact if you type Quantum Magnetism into wikpedia it apparently redirects you straight to "Spin Models" (i.e. Heisenberg model, Hubbard model, etc.)

questionpost

Also, check out virtual particles

Steger

Perhaps we should nail down the question you are asking. Are you curious about the ORIGIN of the magnetic fields you see around you at a quantum level and how magnetic materials acquire them? Or are you wondering if there is a quantum mechanical version of Maxwell's equations? If the former see my previous posts if the latter then magnetism (as one can see from Maxwell's equations) is not a separate entity from the electric field, which is which is simple a matter of perspective (i.e. relative velocity). Thus the quantum version of Maxwell's equations, if you like, (QED) cannot be made to treat magnetism separately from electric fields. They are one and the same and yes they can be quantized and the mediating boson is the photon. Is this what you're after? (this is what jambaugh is describing)

MrRobotoToo

Here's a somewhat simplistic explanation that may help you understand the quantum mechanical origin of the electromagnetic force. Suppose you have a non-relativistic, spinless particle moving freely in empty space. Its behavior is governed by the Schrodinger equation, without any interaction term. A symmetry that is satisfied by the probability distribution of the particle is an arbitrary change of phase of the underlying wave function. This change of phase can itself by a smooth function of space and time. However, it turns out that the Schrodinger equation without an interaction term is not form-invariant when such a phase transformation is performed. One can make the Schrodinger equation form-invariant to such phase transformations by adding extra terms into it. It turns out that the extra terms needed are precisely the vector and scalar potential of electromagnetism! This argument can be made more general and more rigorous--it is known as the Gauge Principle.

jambaugh

Yadda yadda, Read the OP. The context was "is there a magnetic theory analogous to the electric one" which has been clarified for him (until your post obscured the matter.)

I can go into e.g. the Josephson effect but that sheds no light on the basics of quantized electrical fields and charges. Likewise invoking condensed matter phenomena (a topic in and of itself) doesn't shed any light on the basics of the quantum theory of magnetism (which is of course simply the quantum theory of electromagnetism).

The excerpt I quoted and criticized is without merit. To whit...

The fundamental interactions (fundamental, not derivative!) driving the magnetic field is the electromagnetic interaction. As it is one of our two long range forces it has a perfectly compatible classical and quantum description. It is not true that it has "no classical analogue".

The statement you made is false. As I read it either you were anxious to invoke many irrelevant esoteric topics or you were not reading the thread and understanding the level of the OP question. In either event (or for whatever reason you made the statement, still given its fallacy) your statement did not in any way serve the purpose of enlightening the OP or other readers. That is why I jumped on it so firmly.

Yes there are rich areas of research on condensed matter invoking the magnetic component of particle-particle electromagnetic interaction. Beautiful stuff. But it isn't fundamental (to magnetism as an effect) but rather derivative. One must first have the quantum theory of (electro-)magnetic interaction before one can begin the theory of magnetically coupled spin networks, and ferro-,para-,dia-,antiferro-...magnetism in condensed matter systems. Not to mention thermodynamics and quantum stat mec. with particle statistics playing its part.

jambaugh

Before googling "quantum magnetism" please re-read the OP and understand the OP's meaning of the phrase.

henpen

Bickering aside, thanks for enlightening me.