Abstract
We study a class of free local quantum field theories on a flat 10-dimensional space, assuming a symmetry with respect to the symplectic groupSp(4,R) acting on the coordinates through its adjoint representation. These theories describe «particles» that transform according to irreducible unitary representations of an inhomogeneousSp(4,R) group satisfying a spectral condition (positivity of the energy). We give the explicit form of these representations, we construct the corresponding quantum fields and we determine the field equations, the transformation laws, the (anti)commutation relations and the two-point Wightman functions. We discuss the local (anti)commutativity properties of the fields, that are in a strict sense weaker than the ones of the Lorentz-invariant theories, and we find a connection between «spin» and statistics.
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