# Physical degrees of freedom

• JustinLevy
In summary, the concept of "physical" degrees of freedom in physics refers to the number of independent parameters that are needed to fully describe a system. In the case of electromagnetic interactions, there are four degrees of freedom for the four-vector potential, but one of these is not physical and another is a "gauge" freedom. For interactions with higher symmetries, such as the strong force SU(3), the number of physical degrees of freedom can be determined by considering the energy density of a gas of gluons, which is 2 times the dimension of the adjoint representation. Therefore, while there are 8 gluons, only 7 of them are actually physical degrees of freedom.
JustinLevy
"physical" degrees of freedom

Starting with the Lagrangian for EM, it looks like there are four degrees of freedom for the four-vector potential. But one term is not physical in that it can be expressed completely in terms of the other degrees of freedom (so it is not a freedom itself), and there is another "freedom" that is not physical because it doesn't effect the equations of motion (the "gauge" freedom).

For interactions with higher symmetries (like the weak force SU(2), or the strong force SU(3)), is there an easy "symmetry argument" for how many of the components of their "potentials" will actually be physical freedoms?

For example, there are 8 gluons. How many physical degrees of freedom are there actually amongst these 8?

The counting is essentially the same at the linearized level. For example, the energy density of a gas of photons is $$\epsilon/T^4 = \pi^2/15$$ while the energy density for a gas of free SU(N) gluons (at high temperature, say) is $$\epsilon/T^4 = (N^2 - 1) \pi^2/15$$. In other words, you get one photon contribution for each gauge boson. In general, you would have 2 times the dimension of the adjoint representation degrees of freedom.

## 1. What are physical degrees of freedom?

Physical degrees of freedom refer to the number of ways a system can move or change in space. This includes translation (movement), rotation, and vibration.

## 2. How do physical degrees of freedom relate to entropy?

The number of physical degrees of freedom of a system is directly related to its entropy. As the number of degrees of freedom increases, so does the system's entropy, or disorder.

## 3. Can physical degrees of freedom be quantified?

Yes, physical degrees of freedom can be quantified by counting the number of independent parameters needed to fully describe the system's movement or configuration.

## 4. How do physical degrees of freedom impact the behavior of molecules?

The number of physical degrees of freedom of a molecule determines its ability to store and transfer energy, which in turn affects its behavior and properties.

## 5. Can physical degrees of freedom be changed or manipulated?

Yes, physical degrees of freedom can be changed or manipulated through external forces, such as temperature, pressure, or electric fields. This can alter the behavior and properties of the system.

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