We characterise the homogeneous and isotropic gauge invariant and quasifreestates for free Dirac quantum fields on Robertson-Walker spacetimes in any evendimension. Using this characterisation, we construct adiabatic vacuum states oforder $n$ corresponding to some Cauchy surface. We then show that any two suchstates (of sufficiently high order) are locally quasi-equivalent. We propose amicrolocal version of the Hadamard condition for spinor fields on arbitraryspacetimes, which is shown to entail the usual short distance behaviour of thetwopoint function. The polarisation set of these twopoint functions isdetermined from the Dencker connection of the spinorial Klein-Gordon operatorwhich we show to equal the (pull-back) of the spin connection. Finally it isdemonstrated that adiabatic states of infinite order are Hadamard, and thatthose of order $n$ correspond, in some sense, to a truncated Hadamard seriesand will therefore allow for a point splitting renormalisation of the expectedstress-energy tensor.
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