>>11298751How does an off-shell formulation look anyway mathematically? Unlike in the purely bosonic case, you cannot simply construct a space of fields (e. g. as sections of some vector bundle associated to a Spin representation of SO(n-1,1)), since you need to require the odd part of the Super Poincaré algebra to have its Lie bracket in the space of translation.
And what is meant by “degree of freedoms” in this case. Freed in his lecture note said that the on-shell “degrees of freedom” are the dimension of the finite unitary representation of the little group (the reductive part of the stabilizer of an arbitrary element x in an orbit of V* -different type depending whether the particle has mass or not) used in the Wigner classification construction. But in off-shell representation there is obviously no stabilizer of anything. So we are dealing with all of (the covering group of) SO(n-1,1), which obviously isn’t compact and has therefore not finite dimensional unitary representation. What do we mean by degrees of freedom then? How can I employ counting arguments to show the impossibility of maximally supersymmetric off-shell constructions?
