# Particle of M=0, Q=1, S=1/2, Confined?

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• Spinnor
In summary, the conversation discusses the possibility of a mass-less electrically charged particle of spin 1/2 being confined by a hypothetical potential, resulting in a localized massive charged particle at large distances. There is also mention of a quantum random walk and the Higgs mechanism. The idea of interpreting electrons in this way is discussed, as well as the possibility of a particle with spin up or down depending on its momentum vector. The complexity of the proton spin is also mentioned.
Spinnor
Gold Member
Hypothetically, could we have a mass-less electrically charged particle of spin 1/2 confined by a hypothetical potential so that at large distance scales the particle looked like localized massive charged particle of spin 1/2? I'm thinking of a mass-less charged particle that does some kind of speed of light random walk.

Is it possible to interpret electrons this way?

Thanks!

Coincidentally, this is not too far away from how the Higgs mechanism works. There is no confining potential, but the interactions with the background Higgs field. And the "random walk" is a quantum random walk with the particle passing all possible states with different amplitude. Without the Higgs field, the electron would be massless.

However, it is generally simpler to include the mass part of the Lagrangian in the free part when doing perturbation theory.

Spinnor
Can I build on that picture in the following way. In 3 dimensional momentum space plot a very large number of momentum vectors that represents the possible values of momentum this mass-less particle can take. Let all the momentum vectors with a positive (negative) component of momentum in the z direction have right-handed helicity (left-handed helicity), or momentum vectors in the upper half of momentum space are right-handed and momentum vectors in the lower half of momentum space are left-handed.

With such an assignment do I get a particle that is spin up?

Notice if we rotate the above picture 180 degrees about the x or y-axis we get spin down?

A rotation of the above picture 90 degrees around the y-axis gives us 50% spin in +x and 50% spin in -x?

Thanks!

The proton is also an interesting system in that context: tiny masses of the quarks (charged with spin 1/2), confined by QCD, leading to a much larger mass. The proton spin is very complex, and not simply the sum of spins of its valence quarks.

Spinnor

## 1. What is the meaning of M=0, Q=1, S=1/2 in relation to a confined particle?

M, Q, and S represent different quantum numbers that describe the properties of a particle. In this case, M=0 indicates that the particle has zero spin, Q=1 represents a positive charge, and S=1/2 signifies that the particle has a spin of 1/2. These numbers help us understand the behavior and characteristics of the confined particle.

## 2. How is a particle "confined"?

A confined particle is one that is restricted to a specific region or space. This can be due to external forces, such as a magnetic field, or internal forces, such as the particle being bound to another particle. Confined particles have limited movement and can exhibit unique properties compared to particles that are not confined.

## 3. What are the implications of a particle having a spin of 1/2?

A spin of 1/2 is a common characteristic of fundamental particles, such as electrons and quarks. It is a quantum property that describes the intrinsic angular momentum of a particle. The spin of a particle can affect its behavior and interactions with other particles, and is an important factor in understanding the nature of matter.

## 4. How do scientists study confined particles?

There are various methods used to study confined particles, depending on the specific properties of the particle. Some common techniques include scattering experiments, which involve directing particles at the confined particle and analyzing the resulting patterns, and spectroscopy, which uses light or other forms of energy to probe the confined particle and measure its properties.

## 5. Can confined particles have different quantum numbers?

Yes, confined particles can have different combinations of quantum numbers, which can result in unique properties. For example, a particle with M=1, Q=-1, S=1 may have different behaviors compared to a particle with the values M=0, Q=1, S=1/2. The different combinations of quantum numbers can also help scientists classify and categorize particles.

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