haushofer said:Take a look at Van Proeyen's online notes on SUGRA, or his book with Freedman. There it is really explicitly explained, both of-shell and on-shell :)
The Vielbein's DOF's are easy (of-shell): it's a matrix, so it has D^2 components in D dimensions. Local Lorentz transformations make you subtract 1/2*D*(D-1) components from it, leaving you with 1/2*D*(D+1) components for the metric. Which is the right amount for a symmetric tensor like the metric.
The gravitino is a theoretical particle that is predicted by supersymmetric theories. It has a spin of 3/2, which gives it four possible degrees of freedom. However, in some supersymmetric theories, the gravitino's spin may be reduced to 1/2, resulting in two degrees of freedom.
The degree of freedom of a gravitino determines its interactions with other particles. For example, a gravitino with four degrees of freedom can interact with all other particles, while a gravitino with two degrees of freedom may only interact with particles that have spin 1/2 or 1.
Yes, the degree of freedom of a gravitino can change depending on the specific supersymmetric theory being considered. In some theories, the gravitino's spin may be reduced to 1/2, resulting in a decrease in its degrees of freedom.
The degree of freedom of a gravitino is closely related to supersymmetry, as it is a key component of supersymmetric theories. In fact, the gravitino is the supersymmetric partner of the graviton, the particle that mediates the gravitational force.
The degree of freedom of a gravitino is important for understanding the fundamental particles and forces of the universe. It is also relevant for theories such as string theory, which attempts to reconcile gravity with quantum mechanics. By studying the degree of freedom of a gravitino, scientists hope to gain a better understanding of the underlying principles of the universe.