FREE QUANTUM-FIELDS IN 10 DIMENSIONS WITH SP(4,R) SYMMETRY

We study a class of free local quantum field theories on a flat 10-dim ensional space, assuming a symmetry with respect to the symplectic gro up Sp(4,R) acting on the coordinates through its adjoint representatio n. These theories describe <<particles>> that transform according to i rreducible unitary representations of an inhomogeneous Sp(4,R) group s atisfying a spectral condition (positivity of the energy). We give the explicit form of these representations, we construct the correspondin g quantum fields and we determine the field equations, the transformat ion laws, the (anti)commutation relations and the two-point Wightman f unctions. We discuss the local (anti)commutativity properties of the f ields, that are in a strict sense weaker than the ones of the Lorentz- invariant theories, and we find a connection between <<spin>> and stat istics.