Classical electroweak field theory

In summary, the conversation discusses the absence of a classical force corresponding to the weak interaction and the difficulties in describing the classical theory of unstable particles. The reason for this is because the effective range of the weak force is much smaller than the Compton wavelength of low-energy probes, making it hard to isolate the weak interaction. Additionally, the instability of the W/Z bosons further complicates the possibility of a classical electroweak field theory.
  • #1
bcrowell
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A question I'm sure I've seen asked here and/or elsewhere is why there doesn't seem to be any classical force corresponding to the weak interaction. I came up with the following, and am wondering whether this seems correct and satisfying to others.

Basically, being able to write down a Lagrangian density isn't the same thing as being able to describe the classical theory that is the counterpart of a quantized system. In particular, it seems like this can't possibly work for unstable particles. For example, the Lagrangian density for muon decay has a constant in it, GF, the Fermi coupling constant. The half-life of the muon goes like [itex]h/G_F^2[/itex]. In the classical limit, the half-life goes to zero, so the classical theory of muons is a theory with no muons in it.
 
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  • #2
Classical EM would serve quite well to describe the flight of atmospheric muons to a detector at sea level; the finite lifetime is not a significant problem. The reason there is no classical weak force (analogous to Coulomb's law) is because the effective range of the weak force is [itex]r_W \sim 1/M_W[/itex], which is orders of magnitude smaller than the Compton wavelength of any low-energy probe. This is of course ignoring that EM and strong interactions between the probes we do have available would make it hard to isolate the weak interaction in the first place.
 
  • #3
fzero said:
Classical EM would serve quite well to describe the flight of atmospheric muons to a detector at sea level; the finite lifetime is not a significant problem.
I'm talking about the fundamental underlying field theory.

fzero said:
The reason there is no classical weak force (analogous to Coulomb's law) is because the effective range of the weak force is [itex]r_W \sim 1/M_W[/itex], which is orders of magnitude smaller than the Compton wavelength of any low-energy probe.
I'm interested in the reasons why there isn't even in principle any classical electroweak field theory.

(Why would the relevant thing be the Compton wavelength, h/mc, rather than the de Broglie wavelength, h/p, that was relevant?)
 
  • #4
I'm interested in the reasons why there isn't even in principle any classical electroweak field theory.
To have a classical field you need to accumulate a large number of bosons, and the W/Z bosons are unstable.
 

FAQ: Classical electroweak field theory

1. What is classical electroweak field theory?

Classical electroweak field theory is a theoretical framework that describes the electromagnetic and weak nuclear forces as unified aspects of a single fundamental force. It is based on the principles of quantum field theory and special relativity.

2. What are the main components of classical electroweak field theory?

The main components of classical electroweak field theory are the electromagnetic field and the weak nuclear field, which are combined into a single mathematical framework known as the electroweak field. This theory also includes the Higgs field, which is responsible for giving particles their mass.

3. How does classical electroweak field theory explain the behavior of particles?

Classical electroweak field theory explains the behavior of particles by describing them as excitations in the underlying electromagnetic and weak nuclear fields. These particles interact with each other through the exchange of virtual particles, such as photons and W and Z bosons.

4. What experimental evidence supports classical electroweak field theory?

There is a wealth of experimental evidence that supports classical electroweak field theory, including the discovery of the W and Z bosons in the 1980s, which confirm the existence of the weak nuclear force. Other evidence includes the precise predictions of particle interactions made by the theory, which have been confirmed by experiments at the Large Hadron Collider.

5. How does classical electroweak field theory relate to the Standard Model of particle physics?

Classical electroweak field theory is a crucial component of the Standard Model of particle physics, which is the most successful and well-tested theory for explaining the behavior of subatomic particles. In the Standard Model, the electroweak field is combined with the strong nuclear force to form a unified theory of all known fundamental forces.

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