How do we know which is strong,weak force with considering Lagrangian?

In summary, the strength of a force can be determined by looking at its corresponding Lagrangian, which depends on the coupling constant and the form of the theory. The mass of the force carrier boson also affects the range of the force, with a greater mass resulting in a shorter distance of interaction. However, this can be unclear when considering the renormalization group theory and the change in mass with transfer momentum. There are four types of interactions discovered through experiments, each with their own characteristics and self-consistent theories. It is difficult to determine the intensity of a force based on its Lagrangian, as they all have the same form. The weak interaction has a similar coupling constant to the electromagnetic force, but is much weaker in comparison
  • #1
ndung200790
519
0
Please teach me this:
How do we know a force is strong,week or intermediate by considering the corresponding Lagrangian.It seem that the intensiveness depends on both coupling constant,the form of theory(form of Lagrangian).By the way, the mass of force carrier boson stipulates the range of the force. The greater mass the shorter distance of interaction.But there is an unclear for me,because the mass changes when we change transfer momentum as we know in renormalization group theory.
Thank you very much in advance.
 
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  • #2
At the moment,I think that four types of interaction are discovered by experiment.Each type of interaction has many characteristics.And each theory is self-consistent with those characteristics.But it seem that we could not say any thing about the intensiveness of force basing on the Lagrangian,because all Lagrangian have same form:(coupling constant)(boson field)(current of fermion fields).Is that correct?
 
  • #3
The week coupling constant g(of week interaction) has the same order as electromagnetic coupling constant(of QED),then I do not understand why the force of week interaction is very much weeker than electromagnetic force.
 
  • #4
It seem to me that the short distant interaction in general speaking must be the week interaction(when we consider ''macroscopic" level).
 
  • #5
With the meaning that the mass of force carrier boson is large.
 
  • #6
It seem to me that the SU(3) symmetry leads to large coupling constant at large distance and long distance interaction.Then the interaction must be strong interaction.
The week and electromagnetic interactions have the same order of coupling constant,but the week interaction is short distance interaction because of massive boson,then the ''week interaction'' must be the week interaction when we consider ''macro'' level physics.
 

1. How do we determine the strength of the strong and weak forces?

The strength of a force is determined by its coupling constant, which is a measure of how strongly a particle interacts with the force-carrying particles. In the Standard Model of particle physics, the strong force is described by the coupling constant alpha_s, while the weak force is described by the coupling constant g_w. These values are experimentally determined and can be calculated using the Lagrangian, which is a mathematical framework used to describe the interactions between particles.

2. What is the role of the Lagrangian in determining the strength of forces?

The Lagrangian is a mathematical function that describes the dynamics of a system, including the behavior of particles and their interactions. In the Standard Model, the Lagrangian is used to calculate the strength of the strong and weak forces, as well as other fundamental forces such as electromagnetism and gravity. By studying the Lagrangian, scientists can determine the strength of these forces and make predictions about particle interactions.

3. How does the Lagrangian help us understand the differences between the strong and weak forces?

One of the key differences between the strong and weak forces is their range. The strong force has a very short range, only acting over distances of about 10^-15 meters, while the weak force can act over much longer distances, up to about 10^-18 meters. The Lagrangian helps us understand these differences by describing the interactions between particles at different distances, and how these interactions change with distance.

4. Can the Lagrangian predict the strength of forces at different energies?

Yes, the Lagrangian can be used to predict how the strength of the strong and weak forces change at different energies. This is because the coupling constants for these forces are not constant, but instead vary with energy. This phenomenon is known as "running" of the coupling constants, and it is an important feature of the Standard Model that can be studied and tested through experiments at different energy levels.

5. Are there any limitations to using the Lagrangian to determine the strength of forces?

While the Lagrangian is a powerful tool for understanding the strength of forces, it does have its limitations. One limitation is that it only applies to the Standard Model of particle physics, and may not accurately describe interactions at very high energies or on very small scales. Additionally, the Lagrangian is a mathematical abstraction and does not fully capture the complexity of particle interactions, so it must be combined with experimental data to make accurate predictions about the strength of forces.

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