Questions about some basic conceptions

[isospin]

Here I have some questions when reading a paper on supersymmetry. I am not familiar with those phrases below.
1, what is called 'rigid symmetry'?
2, does 'propagating degrees of freedom' mean degrees of freedom on shell?
3, when one says 'the gauge field are not dynamical', does it mean it has no degree of freedom on shell?

Thanks.

 

[nrqed]

Here I have some questions when reading a paper on supersymmetry. I am not familiar with those phrases below.
1, what is called 'rigid symmetry'?

I think this is used only in the context of SUSY.
It's another name for "global supersymmetry", i.e. the SUSY parameter does not depend on spacetime.

2, does 'propagating degrees of freedom' mean degrees of freedom on shell?

I think so.

3, when one says 'the gauge field are not dynamical', does it mean it has no degree of freedom on shell?

Thanks.

Are you sure you don't mean "auxiliary field" instead of gauge field? An auxiliary field is not dynamical because, as you said, it has no on-shell degrees of freedom.

 

[Entropia]

1. Rigid symmetry refers to a type of symmetry in physics where the symmetry transformation does not depend on the coordinates of spacetime. This means that the laws of physics remain the same regardless of where or when they are applied. In supersymmetry, rigid symmetry refers to a symmetry between bosons (particles with integer spin) and fermions (particles with half-integer spin).

2. Yes, propagating degrees of freedom are degrees of freedom that can propagate and interact with other particles in a theory. This term is often used in quantum field theory where particles are described as excitations of fields. On-shell refers to the condition where the equations of motion are satisfied, so propagating degrees of freedom on-shell means that they satisfy the equations of motion.

3. When someone says that the gauge fields are not dynamical, it means that they do not have their own independent degrees of freedom. In gauge theories, the gauge fields are not considered to be physical particles, but rather mathematical constructs that describe the interactions between physical particles. This means that they do not have degrees of freedom on-shell, as they are not considered to be physical particles.

 

[Entropia]

1. Rigid symmetry refers to a type of symmetry in which the transformation of the system does not depend on the coordinates or time. In other words, the symmetry is independent of the specific values of the variables in the system. This type of symmetry is important in theories like supersymmetry, where it plays a role in relating different types of particles.

2. Yes, "propagating degrees of freedom" usually refers to the degrees of freedom that are physically relevant and contribute to the dynamics of the system. In the context of supersymmetry, this would typically refer to the degrees of freedom of the particles that are actually propagating in the theory.

3. When someone says that the gauge fields are not dynamical, it means that they do not have their own independent degrees of freedom. Instead, they are determined by other fields in the theory. In supersymmetry, this is often the case for the gauge fields, as they are typically determined by the superpartner fields. This does mean that they have no degrees of freedom on shell, as they can still contribute to the dynamics of the system through their interactions with other fields.