M. Toller, FREE QUANTUM-FIELDS IN 10 DIMENSIONS WITH SP(4,R) SYMMETRY, Nuovo cimento della Societa italiana di fisica. B, Relativity, classical and statistical physics, 108(3), 1993, pp. 245-274
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.